CN117252131B - Numerical simulation method and device suitable for thin-wall structure - Google Patents
Numerical simulation method and device suitable for thin-wall structure Download PDFInfo
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Abstract
The application relates to the technical field of numerical simulation, in particular to a numerical simulation method and device suitable for a thin-wall structure, which are used for improving the calculation efficiency of numerical simulation of the thin-wall structure. The scheme is as follows: determining a fixed wall boundary of the thin-wall structure, and determining a grid with a minimum distance Level-Set value from the grid to the fixed wall boundary meeting preset conditions; according to the Level-Set value, calculating the field variables which meet preset condition grids; when the fluid particles are close to the solid wall boundary, calculating the field variable of the fluid particles according to the field variable of the grid; the fluid particles close to the solid wall boundary are subjected to the completion of a momentum conservation equation and a missing item of a mass conservation equation through the physical properties and the field variables of the fluid particles, so that the final acceleration and the density change rate of the fluid particles are obtained; time integration is carried out on the acceleration and the density change rate obtained through calculation, and new fluid particle positions and fluid particle densities are obtained; the position and velocity of the fluid particles are corrected.
Description
Technical Field
The present disclosure relates to the field of numerical simulation technologies, and in particular, to a numerical simulation method and apparatus suitable for a thin-wall structure.
Background
Numerical simulation is an important means for researching the interaction of fluid and a structure, and physical quantities which cannot be obtained through experiments can be obtained through the numerical simulation. For the simulation of thin-walled structures, the smooth fluid particle hydrodynamic method (Smoothed Particle Hydrodynamics, SPH) is one of the most dominant numerical simulation methods.
The SPH method uses fluid particles to characterize a fluid, and the conventional SPH boundary condition method requires additional creation of virtual fluid particles to characterize a boundary, which may have a certain thickness due to a certain size of the virtual fluid particles. When the boundary thickness of the thin-walled structure is very small (such as a thin-walled baffle, a stirring paddle, etc.), the size of the fluid particles corresponding to the boundary thickness needs to be small enough to perform numerical simulation, which will make the total number of fluid particles of the thin-walled structure large, thereby reducing the calculation efficiency of the numerical simulation of the thin-walled structure.
Disclosure of Invention
In view of the foregoing, the present application provides a numerical simulation method and apparatus suitable for a thin-walled structure, for improving the calculation efficiency of numerical simulation of the thin-walled structure.
In a first aspect, an embodiment of the present application provides a numerical simulation method applicable to a thin-wall structure, where the method includes:
step S1, determining a calculation domain according to the geometric dimension of a model file of a thin-wall structure, dividing the calculation domain into grids, determining a fixed wall boundary of the thin-wall structure, and determining a grid with a minimum distance Level-Set value meeting preset conditions from the grid to the fixed wall boundary; the Level-Set value of the solid wall boundary of the thin-wall structure is 0, and the ratio of the thickness of the solid wall boundary of the thin-wall structure to the size of the fluid particles is less than 4;
s2, calculating field variables which meet preset condition grids according to the Level-Set value;
s3, when the fluid particles are close to the fixed wall boundary, calculating the field variable of the fluid particles according to the field variable of the grid;
s4, supplementing the fluid particles close to the solid wall boundary with a momentum conservation equation and a missing item of the mass conservation equation through the physical properties and the field variables of the fluid particles to obtain the final acceleration and the density change rate of the fluid particles;
s5, performing time integration on the acceleration and the density change rate obtained by the calculation in the step S4 to obtain new fluid particle positions and fluid particle densities; if the Level-Set value of the new fluid particle position is smaller than a preset value, correcting the position and the speed of the fluid particle to obtain a corrected displacement field and a corrected speed field;
and S6, repeating the steps S3-S5, so that the numerical simulation whole process solving of the thin-wall structure is completed.
In an optional embodiment of the present invention, the step S1 of determining a calculation domain according to a geometric dimension of a model file of a thin-wall structure, performing grid division on the calculation domain, determining a solid wall boundary of the thin-wall structure, and determining a grid with a minimum distance Level-Set value from the grid to the solid wall boundary meeting a preset condition, includes:
importing a thin-wall structure model file of a fixed wall boundary, defining a geometric bounding box of the model according to a coordinate value range of the model file, and meshing a space in the bounding box;
calculating the Level-Set value of each grid, and enabling the Level-Set value to be smaller than or equal tokh+ dxAnd a grid greater than or equal to 0 is determined as a grid meeting preset conditions, the grid is provided with a grid patternkIs the smooth length coefficient of the SPH method, thehIs of smooth radius, dxIs a gridSize.
In an optional embodiment of the present invention, the step S2 of calculating, according to the Level-Set value, field variables of each grid meeting preset conditions includes:
if the field variable which accords with the preset condition grid is a unit normal vector, calculating the unit normal vector which accords with the preset condition grid through the following formula;
wherein,is the unit normal vector of the grid, +.>For the Level-Set value of the grid, +.>For the Nabla operator, the gradient is represented.
In an optional embodiment of the present invention, the step S2 of calculating, according to the Level-Set value, field variables of each grid meeting preset conditions includes:
if the field variable meeting the preset condition grid is a kernel function missing value and a kernel function gradient missing value, the field variable is obtained by the following smooth functionHComputing gridbFor the center grid meeting preset conditionscIs a contribution of (1):
wherein,is thatbThe temporary value of the number grid Level-Set is expressed as follows:
central grid meeting preset conditionscThe kernel missing values of (2) are:
central grid meeting preset conditionscThe kernel gradient missing values are:
wherein,Dthe dimensions of the problem are represented and,for nuclear function value->Gradient values for the kernel function.
In an alternative embodiment provided by the present invention, step S3, when a fluid particle approaches the solid wall boundary, calculates a field variable of the fluid particle according to a field variable of the grid, including:
according to the coordinates of the fluid particles, acquiring indexes and direction weight values of grid center points around the fluid particles;
and calculating the field variable of the fluid particles through the field variable of the grid corresponding to the index of the central point of the surrounding grid and the direction weight value.
In an optional embodiment of the present invention, the calculating the field variable of the fluid particle by the field variable of the grid corresponding to the index of the center point of the surrounding grid and the direction weight value includes:
when the problem is a three-dimensional problem, an index of grid center points around the fluid particles is obtainedi,j,kWeight values in three directions；
For the field variable of the fluid particles, firstly, pairxInterpolation is carried out on the direction, and the following steps are obtained:
re-pairingyInterpolation is carried out on the direction to obtain:
finally tozInterpolation is carried out on the direction to obtain:
wherein,is the field variable of the fluid particle, +.>、/>、/>、/>、/>、/>、、/>Corresponding field variables are indexed for 8 grid center points around the fluid particle.
In an optional embodiment of the present invention, the calculating the field variable of the fluid particle by the field variable of the grid corresponding to the index of the center point of the surrounding grid and the direction weight value includes:
when the problem is a two-dimensional problem, an index of grid center points around the fluid particles is obtainedi,jWeight values in two directions；
For the field variable of the fluid particles, firstly, pairxInterpolation is carried out on the direction, and the following steps are obtained:
re-pairingyInterpolation is carried out on the direction to obtain:
wherein,for the field variable of the fluid particles, +.>，/>，/>，/>Corresponding field variables are indexed for the 4 grid center points around the fluid particle.
In an optional embodiment provided by the present invention, the step S4 of complementing the missing term of the momentum conservation equation and the mass conservation equation of the fluid particle near the solid wall boundary by the physical property and the field variable of the fluid particle to obtain the final acceleration and the density change rate of the fluid particle includes:
the final acceleration and density change rate of the fluid particles is calculated by the following formula:
wherein,representing the derivative of the substance>For density change rate>For final acceleration +.>For the density of fluid particles a>For the pressure of fluid particles a>Is the velocity of fluid particle a; superscript-indicates that the entry is a boundary complement entry, < ->The value of the gradient absence of the kernel function in the field variable for the fluid particle a.
In an optional embodiment provided by the present invention, the step S5 is to perform time integration on the acceleration and the density change rate calculated in the step S4 to obtain a new fluid particle position and a new fluid particle density; if the Level-Set value of the new fluid particle position is smaller than the preset value, correcting the position and the speed of the fluid particle to obtain a corrected displacement field and a corrected speed field, wherein the method comprises the following steps:
the position and velocity of the fluid particles are corrected by the following correction formula:
wherein, superscriptRepresenting the corrected value, ++>A displacement vector corrected for fluid particle a, +.>、/>Position and velocity before correction of fluid particles a, respectively, < >>、/>Normal vector and Level-Set values of fluid particle a, respectively, +.>Integrating the time step; />Is the fluid inter-particle distance.
In a second aspect, an embodiment of the present application provides a numerical simulation apparatus suitable for a thin-walled structure, the apparatus including:
the determining module is used for determining a calculation domain according to the geometric dimension of the model file of the thin-wall structure, dividing the calculation domain into grids, determining a fixed wall boundary of the thin-wall structure, and determining a grid with a minimum distance Level-Set value meeting preset conditions from the grid to the fixed wall boundary; the Level-Set value of the solid wall boundary of the thin-wall structure is 0, and the ratio of the thickness of the solid wall boundary of the thin-wall structure to the size of the fluid particles is less than 4;
the calculation module is used for calculating the field variables which accord with the preset condition grids according to the Level-Set value;
the calculation module is further used for calculating a field variable of the fluid particles according to the field variable of the grid when the fluid particles are close to the fixed wall boundary;
the calculation module is further used for supplementing the fluid particles close to the solid wall boundary with the loss terms of the momentum conservation equation and the mass conservation equation through the field variables of the fluid particles to obtain the final acceleration and the density change rate of the fluid particles;
the calculation module is also used for carrying out time integration on the acceleration and the density change rate obtained by calculation to obtain new fluid particle positions and fluid particle densities; if the Level-Set value of the new fluid particle position is smaller than a preset value, correcting the position and the speed of the fluid particle to obtain a corrected displacement field and a corrected speed field; and completing the numerical simulation whole process solving of the thin-wall structure.
According to the numerical simulation method suitable for the thin-wall structure, a calculation domain is determined according to the geometric dimension of a model file of the thin-wall structure, grid division is conducted on the calculation domain, a fixed wall boundary of the thin-wall structure is determined, and a grid with a minimum distance Level-Set value meeting preset conditions from the grid to the fixed wall boundary is determined; according to the Level-Set value, calculating the field variables which meet preset condition grids; when the fluid particles are close to the solid wall boundary, calculating the field variable of the fluid particles according to the field variable of the grid; the fluid particles close to the solid wall boundary are subjected to the completion of a momentum conservation equation and a missing item of a mass conservation equation through the physical properties and the field variables of the fluid particles, so that the final acceleration and the density change rate of the fluid particles are obtained; time integration is carried out on the acceleration and the density change rate obtained through calculation, and new fluid particle positions and fluid particle densities are obtained; if the Level-Set value of the new fluid particle position is smaller than a preset value, correcting the position and the speed of the fluid particle to obtain a corrected displacement field and a corrected speed field; repeating the steps to finish the numerical simulation whole process solution of the thin-wall structure. The traditional method for creating the virtual fluid particle to represent the solid wall boundary at least needs to use 2 virtual particles in the thickness direction, and because fluid possibly exists at two sides of the boundary, at least 4 virtual particles are used for representing the solid wall boundary in the thickness direction, if the thickness of the solid wall boundary is smaller than that of the 4 virtual particles, the solid wall boundary at two sides can be influenced by the fluid particles, namely, the method for creating the virtual fluid particle to represent the solid wall boundary is used, when the ratio of the thickness of the solid wall boundary of the thin-wall structure to the size of the fluid particle is smaller than 4, the simulation result is inaccurate, the determination of the Level-Set value of 0 is used as the solid wall boundary of the thin-wall structure, namely, the Level-Set value is used for implicitly representing the solid wall boundary, the interaction of the fluid particle is not needed to be generated in the boundary area, and the interaction of the single-layer thin-wall structure and the fluid particle can be accurately represented by adopting the full positive Level-Set value, and when the ratio of the thickness of the solid wall boundary of the thin-wall structure to the fluid particle size of the thin-wall structure is smaller than 4, the numerical simulation result of the thin-wall structure can be ensured, and the numerical simulation result of the thin-wall structure can be improved, and the numerical simulation efficiency of the numerical simulation result of the thin-wall structure can be improved.
In order to make the above objects, features and advantages of the present application more comprehensible, preferred embodiments accompanied with figures are described in detail below.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are needed in the embodiments will be briefly described below, it being understood that the following drawings only illustrate some embodiments of the present application and therefore should not be considered limiting the scope, and that other related drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a numerical simulation method applicable to a thin-walled structure according to an embodiment of the present disclosure;
FIG. 2 is a schematic diagram of kernel boundary completion provided in an embodiment of the present application;
FIG. 3 is a schematic diagram of tri-linear interpolation of fluid particles in a Level-Set grid provided in an embodiment of the present application;
FIG. 4 is a schematic diagram of a Level-Set field when the embodiment of the present application is applied to a dam break impact inclined thin-wall baffle simulation model;
FIG. 5 is a diagram of simulation results of a dam break impact inclined thin-wall baffle process according to an embodiment of the present application;
fig. 6 is a block diagram of a numerical simulation apparatus suitable for a thin-wall structure according to an embodiment of the present application.
Detailed Description
The terms first, second, third and the like in the description and in the claims and in the above drawings are used for distinguishing between different objects and not necessarily for describing a particular sequential or chronological order.
In the embodiments of the present application, words such as "exemplary" or "such as" are used to mean serving as examples, illustrations, or descriptions. Any embodiment or design described herein as "exemplary" or "for example" should not be construed as preferred or advantageous over other embodiments or designs. Rather, the use of words such as "exemplary" or "such as" is intended to present related concepts in a concrete fashion that may be readily understood.
In the description of the present application, unless otherwise indicated, "/" means that the associated object is an "or" relationship, e.g., a/B may represent a or B; the term "and/or" in this application is merely an association relation describing an association object, and means that three kinds of relations may exist, for example, a and/or B may mean: there are three cases, a alone, a and B together, and B alone, wherein a, B may be singular or plural. Also, in the description of the present application, unless otherwise indicated, "a plurality" means two or more than two. "at least one of" or the like means any combination of these items, including any combination of single item(s) or plural items(s). For example, at least one (one) of a, b, or c may represent: a, b, c, a-b, a-c, b-c, or a-b-c, wherein a, b, c may be single or plural.
In the embodiments of the present application, at least one may also be described as one or more, and a plurality may be two, three, four or more, which is not limited in this application.
As shown in fig. 1, an embodiment of the present application provides a numerical simulation method applicable to a thin-walled structure, where the numerical simulation method applicable to a thin-walled structure provided in the present application may include:
step S1, determining a calculation domain according to the geometric dimension of a model file of the thin-wall structure, dividing the calculation domain into grids, determining a fixed wall boundary of the thin-wall structure, and determining a grid with a minimum distance Level-Set value meeting preset conditions from the grid to the fixed wall boundary.
The Level-Set value of the solid wall boundary of the thin-wall structure is 0, and the ratio of the thickness of the solid wall boundary of the thin-wall structure to the fluid particle size is less than 4.
Firstly leading in a model file of a thin-wall structure, wherein the model file of the thin-wall structure can be a universal CAD graphic file such as stl or obj, after the model file of the thin-wall structure is led in, determining a calculation domain according to the geometric dimension of the model file of the thin-wall structure, and dividing grids of the calculation domainIs fluid inter-particle distance->1/3 or less of (a). And finally, calculating the minimum distance between each grid and the boundary, wherein the distance is a Level-Set value.
Specifically, step S1, determining a calculation domain according to a geometric dimension of a model file of a thin-wall structure, performing grid division on the calculation domain, determining a solid wall boundary of the thin-wall structure, and determining a grid with a minimum distance Level-Set value from the grid to the solid wall boundary meeting a preset condition, where the step includes:
step S11, importing a model file of the thin-wall structure, defining a geometric bounding box of the model according to a coordinate value range of the model file, and meshing a space in the bounding box.
Step S12, calculating the Level-Set value of each grid, and enabling the Level-Set value to be smaller than or equal tokh+ dxAnd a grid of 0 or more is determined as a grid conforming to a preset condition.
In this embodiment, the space within the boundary narrowband is meshed, the Level-Set value of each mesh is calculated, and the Level-Set value is expressed asThis->The value does not distinguish between the inner or outer sides of the border, i.e +.>Not less than 0; finally, record only +.>≤kh+ dxIs to->≤kh+ dxAnd->And determining the grids which are more than or equal to 0 as grids which meet preset conditions.
Wherein the saidkIs the smooth length coefficient of the SPH method, thehIs of smooth radius, dxFor mesh size, the product of the two is the support domain radius.
Relative to conventional Level-Set field passingThe positive and negative values represent the inside and outside of the boundary, and cannot simulate the solid wall boundary with fluid particles on both sides of the boundary, in this embodiment, an all positive Level-Set field is adopted, namely +.>And 0 is equal to or more than constant, so that the interaction between the solid wall boundary and the fluid particles can be accurately represented through the embodiment.
And S2, calculating field variables which meet preset condition grids according to the Level-Set value.
The field variable at least includes a unit normal vector, a kernel function missing value, a kernel function gradient missing value, and the like, which is not particularly limited in this embodiment.
In an optional embodiment provided in the application, step S2, calculating, according to the Level-Set value, field variables of each grid meeting preset conditions, includes:
if the field variable which accords with the preset condition grid is a unit normal vector, calculating the unit normal vector which accords with the preset condition grid through the following formula;
wherein,is the unit normal vector of the grid, +.>For the Level-Set value of the grid, +.>For the Nabla operator, the gradient is represented.
Taking three dimensions as an example, a central difference method is adopted, and a calculation formula of a normal vector is as follows:
wherein the subscripti,j,kCoordinate index, subscript, representing gridx,y,zRepresenting three components of the vector along the coordinate axes.
In another optional embodiment provided in the application, the step S2 of calculating the field variables of each grid meeting the preset conditions according to the Level-Set value includes:
if the field variables of the grid meeting the preset conditions are kernel function missing values and kernel function gradient missing values, as shown in FIG. 2, the center grid meeting the preset conditions is marked ascTo the central grid meeting preset conditionscDistance is less thankhIs written as a grid of (2)bThe method comprises the steps of carrying out a first treatment on the surface of the If it isbAnd (3) withcLocated on the same side of the boundary (in the figureX), then tocNo contribution; if it isbIs entirely located atcIs on the opposite side (in the figure)) Then paircContributing to the fact; if it isbIs crossed by the boundary (∈ and in the figurecPossibly ipsilateral or heterolateral), then tocA partial contribution; to express the contribution, the contribution is expressed by the following smoothing functionHComputing gridbFor the center grid meeting preset conditionscIs a contribution of (1):
wherein,is thatbThe temporary value of the number grid Level-Set is expressed as follows:
central grid meeting preset conditionscThe kernel missing values of (2) are:
central grid meeting preset conditionscThe kernel gradient missing values are:
wherein,Dthe dimension representing the problem, two dimensions of 2, three dimensions of 3,for nuclear function value->Gradient values for the kernel function.
And S3, when the fluid particles are close to the solid wall boundary, calculating the field variable of the fluid particles according to the field variable of the grid.
In the present embodiment, the solution of the conservation of momentum equation and the conservation of mass equation is performed for the entire calculation domain. When the fluid particles enter a narrow-band range near the solid wall boundary, the field variable of the fluid particles is calculated through bilinear interpolation (two-dimensional) or trilinear interpolation (three-dimensional), and the field variable of the fluid particles comprises a Level-Set value, a unit normal vector, a kernel function gradient missing value and the like.
In an alternative embodiment provided herein, step S3, when the fluid particle approaches the solid wall boundary, calculates a field variable of the fluid particle from the field variable of the grid, including:
step S31, according to the coordinates of the fluid particles, the index and the direction weight value of the central points of the grids around the fluid particles are obtained.
Step S32, calculating the field variable of the fluid particles through the field variable and the direction weight value of the grid corresponding to the index of the central point of the surrounding grid.
Specifically, the calculating the field variable of the fluid particle by the field variable of the grid corresponding to the index of the surrounding grid center point and the direction weight value includes:
as shown in fig. 3, if the tri-linear interpolation (three-dimensional) is used, the index of the center point of the grid around the fluid particle is obtainedi,j,kWeight values in three directions；
For the field variable of the fluid particles, firstly, pairxInterpolation is carried out on the direction, and the following steps are obtained:
re-pairingyInterpolation is carried out on the direction to obtain:
finally tozInterpolation is carried out on the direction to obtain:
wherein,is the field variable of the fluid particle a, +.>、/>、/>、/>、/>、/>、、/>Corresponding field variables are indexed for 8 grid center points around the fluid particle a.
Specifically, the calculating the field variable of the fluid particle by the field variable of the grid corresponding to the index of the surrounding grid center point and the direction weight value includes:
by bilinear interpolation (two-dimensional), the index of the grid center points around the fluid particles is obtainedi,jWeight values in two directions；
For the field variable of the fluid particles, firstly, pairxInterpolation is carried out on the direction, and the following steps are obtained:
re-pairingyInterpolation is carried out on the direction to obtain:
wherein,is the field variable of the fluid particle a, +.>，/>，/>，/>Corresponding field variables are indexed for the 4 grid center points around the fluid particle.
In this embodiment, since the unit normal vector, the kernel function missing value, the kernel function gradient missing value, and the like are calculated and stored before the simulation is performed, and are obtained directly through interpolation when the boundary complement term of the fluid particle momentum equation and the mass equation is solved, the calculation efficiency of the fluid region in the boundary narrowband region can be greatly improved through this embodiment.
And S4, complementing the missing items of the momentum conservation equation and the mass conservation equation of the fluid particles close to the solid wall boundary through the physical properties and the field variables of the fluid particles, and obtaining the final acceleration and the density change rate of the fluid particles.
And (3) supplementing the missing values of the kernel function and the gradient missing values of the kernel function, which are obtained by interpolation calculation in the step (S3), of the fluid particles close to the boundary by using a momentum conservation equation and a missing item of a mass conservation equation, and obtaining the final acceleration and the density derivative of the fluid particles along with time, wherein the derivative is as follows:
in an optional embodiment provided in the present application, the step S4 of complementing the missing term of the momentum conservation equation and the mass conservation equation of the fluid particle near the solid wall boundary by the physical property and the field variable of the fluid particle to obtain the final acceleration and the density change rate of the fluid particle includes:
the final acceleration and density change rate of the fluid particles is calculated by the following formula:
wherein,representing the derivative of the substance>For density change rate>For final acceleration +.>For the density of fluid particles a>For the pressure of fluid particles a>Is the velocity of fluid particle a; superscript-indicates that the entry is a boundary complement entry, < ->The value of the gradient absence of the kernel function in the field variable for the fluid particle a.
S5, performing time integration on the acceleration and the density change rate obtained by the calculation in the step S4 to obtain new fluid particle positions and fluid particle densities; and if the Level-Set value of the new fluid particle position is smaller than the preset value, correcting the position and the speed of the fluid particle to obtain a corrected displacement field and a corrected speed field.
In an alternative embodiment provided in the present application, the acceleration and the density change rate calculated in the step S4 are integrated in time to obtain a new fluid particle position and a new fluid particle density; if the Level-Set value of the new fluid particle position is smaller than the preset value, correcting the position and the speed of the fluid particle to obtain a corrected displacement field and a corrected speed field, wherein the method comprises the following steps:
the position and velocity of the fluid particles are corrected by the following correction formula:
wherein, superscriptRepresenting the corrected value, ++>A displacement vector corrected for fluid particle a, +.>、/>Position and velocity before correction of fluid particles a, respectively, < >>、/>Normal vector and Level-Set values of fluid particle a, respectively, +.>Integrating the time step; />Is the fluid inter-particle distance.
And S6, repeating the steps S3-S5, so that the numerical simulation whole process solving of the thin-wall structure is completed.
Compared with the existing SPH boundary condition method, the method adopts the Level-Set field to represent the solid wall boundary of the thin-wall structure, fluid particles are not required to be generated on the solid wall boundary, and the representation precision of the solid wall boundary is improved; and the traditional Level-Set field passesThe positive and negative values represent the inside and outside of the solid wall boundary, and the thin wall structure with fluid particles on both sides of the solid wall boundary cannot be simulated; the invention adopts an all positive Level-Set field, namely +.>And the constant value is equal to or more than 0, so that the interaction between the thin-wall structure and the fluid particles can be accurately represented.
According to the numerical simulation method suitable for the thin-wall structure, a calculation domain is determined according to the geometric dimension of a model file of the thin-wall structure, grid division is conducted on the calculation domain, a fixed wall boundary of the thin-wall structure is determined, and a grid with a minimum distance Level-Set value meeting preset conditions from the grid to the fixed wall boundary is determined; according to the Level-Set value, calculating the field variables which meet preset condition grids; when the fluid particles are close to the solid wall boundary, calculating the field variable of the fluid particles according to the field variable of the grid; the fluid particles close to the solid wall boundary are subjected to the completion of a momentum conservation equation and a missing item of a mass conservation equation through the physical properties and the field variables of the fluid particles, so that the final acceleration and the density change rate of the fluid particles are obtained; time integration is carried out on the acceleration and the density change rate obtained through calculation, and new fluid particle positions and fluid particle densities are obtained; if the Level-Set value of the new fluid particle position is smaller than a preset value, correcting the position and the speed of the fluid particle to obtain a corrected displacement field and a corrected speed field; repeating the steps to finish the numerical simulation whole process solution of the thin-wall structure. The traditional method for creating the virtual fluid particle to represent the solid wall boundary at least needs to use 2 virtual particles in the thickness direction, and because fluid possibly exists at two sides of the boundary, at least 4 virtual particles are used for representing the solid wall boundary in the thickness direction, if the thickness of the solid wall boundary is smaller than that of the 4 virtual particles, the solid wall boundary at two sides can be influenced by the fluid particles, namely, the method for creating the virtual fluid particle to represent the solid wall boundary is used, when the ratio of the thickness of the solid wall boundary of the thin-wall structure to the size of the fluid particle is smaller than 4, the simulation result is inaccurate, the determination of the Level-Set value of 0 is used as the solid wall boundary of the thin-wall structure, namely, the Level-Set value is used for implicitly representing the solid wall boundary, the interaction of the fluid particle is not needed to be generated in the boundary area, and the interaction of the single-layer thin-wall structure and the fluid particle can be accurately represented by adopting the full positive Level-Set value, and when the ratio of the thickness of the solid wall boundary of the thin-wall structure to the fluid particle size of the thin-wall structure is smaller than 4, the numerical simulation result of the thin-wall structure can be ensured, and the numerical simulation result of the thin-wall structure can be improved, and the numerical simulation efficiency of the numerical simulation result of the thin-wall structure can be improved.
In an embodiment, a numerical simulation device for a thin-walled structure is provided, where the numerical simulation device for a thin-walled structure corresponds to the numerical simulation method for a thin-walled structure. As shown in fig. 6, the numerical simulation apparatus applied to a thin-walled structure includes:
the determining module 61 is configured to determine a calculation domain according to a geometric dimension of a model file of the thin-wall structure, divide the calculation domain into grids, determine a fixed wall boundary of the thin-wall structure, and determine a grid with a minimum distance Level-Set value from the grid to the fixed wall boundary meeting a preset condition; the Level-Set value of the solid wall boundary of the thin-wall structure is 0, and the ratio of the thickness of the solid wall boundary of the thin-wall structure to the size of the fluid particles is less than 4;
the calculation module 62 is configured to calculate, according to the Level-Set value, field variables that each meet a preset condition grid;
the calculation module 62 is further configured to calculate a field variable of the fluid particle according to the field variable of the grid when the fluid particle approaches the solid wall boundary;
the calculation module 62 is further configured to complement, by a field variable of the fluid particle, a momentum conservation equation and a missing term of a mass conservation equation of the fluid particle near the solid wall boundary, so as to obtain a final acceleration and a density change rate of the fluid particle;
the calculating module 62 is further configured to time integrate the calculated acceleration and density change rate to obtain a new fluid particle position and a new fluid particle density; if the Level-Set value of the new fluid particle position is smaller than a preset value, correcting the position and the speed of the fluid particle to obtain a corrected displacement field and a corrected speed field; and completing the numerical simulation whole process solving of the thin-wall structure.
In an alternative embodiment provided by the present invention, the determining module 61 is specifically configured to:
importing a thin-wall structure model file of a fixed wall boundary, defining a geometric bounding box of the model according to a coordinate value range of the model file, and meshing a space in the bounding box;
calculating the Level-Set value of each grid, and enabling the Level-Set value to be smaller than or equal tokh+ dxAnd a grid greater than or equal to 0 is determined as a grid meeting preset conditions, the grid is provided with a grid patternkIs the smooth length coefficient of the SPH method, thehIs of smooth radius, dxIs a mesh size.
In an alternative embodiment provided by the present invention, the calculating module 62 is specifically configured to:
if the field variable which accords with the preset condition grid is a unit normal vector, calculating the unit normal vector of each grid which accords with the preset condition through the following formula;
wherein,is the unit normal vector of the grid, +.>For the Level-Set value of the grid, +.>For the Nabla operator, the gradient is represented.
In an alternative embodiment provided by the present invention, the calculating module 62 is specifically configured to:
if the field variable meeting the preset condition grid is a kernel function missing value and a kernel function gradient missing value, the field variable is obtained by the following smooth functionHComputing gridbFor the center grid meeting preset conditionscIs a contribution of (1):
wherein,is thatbThe temporary value of the number grid Level-Set is expressed as follows:
central grid meeting preset conditionscThe kernel missing values of (2) are:
/>
central grid meeting preset conditionscThe kernel gradient missing values are:
wherein,Dthe dimensions of the problem are represented and,for nuclear function value->Gradient values for the kernel function.
In an alternative embodiment provided by the present invention, the calculating module 62 is specifically configured to:
according to the coordinates of the fluid particles, acquiring indexes and direction weight values of grid center points around the fluid particles;
and calculating the field variable of the fluid particles through the field variable of the grid corresponding to the index of the central point of the surrounding grid and the direction weight value.
In an alternative embodiment provided by the present invention, the calculating module 62 is specifically configured to:
when the problem is a three-dimensional problem, an index of grid center points around the fluid particles is obtainedi,j,kWeight values in three directions；
For the field variable of the fluid particles, firstly, pairxInterpolation is carried out on the direction, and the following steps are obtained:
re-pairingyInterpolation is carried out on the direction to obtain:
finally tozInterpolation is carried out on the direction to obtain:
wherein,is the field variable of the fluid particle, +.>、/>、/>、/>、/>、/>、、/>Corresponding field variables are indexed for 8 grid center points around the fluid particle.
In an alternative embodiment provided by the present invention, the calculating module 62 is specifically configured to:
when the problem is a two-dimensional problem, an index of grid center points around the fluid particles is obtainedi,jWeight values in two directions；
For the field variable of the fluid particles, firstly, pairxInterpolation is carried out on the direction, and the following steps are obtained:
re-pairingyInterpolation is carried out on the direction to obtain:
wherein,for the field variable of the fluid particles, +.>，/>，/>，/>Corresponding field variables are indexed for the 4 grid center points around the fluid particle. />
In an alternative embodiment provided by the present invention, the calculating module 62 is specifically configured to:
the final acceleration and density change rate of the fluid particles is calculated by the following formula:
wherein,representing the derivative of the substance>For density change rate>For final acceleration +.>For the density of fluid particles a>Is fluid particle aPressure of->Is the velocity of fluid particle a; superscript-indicates that the entry is a boundary complement entry, < ->The value of the gradient absence of the kernel function in the field variable for the fluid particle a.
In an alternative embodiment provided by the present invention, the calculating module 62 is specifically configured to:
the position and velocity of the fluid particles are corrected by the following correction formula:
wherein, superscriptRepresenting the corrected value, ++>A displacement vector corrected for fluid particle a, +.>、/>Position and velocity before correction of fluid particles a, respectively, < >>、/>Normal vector and Level-Set values of fluid particle a, respectively, +.>Integrating the time step; />Is the fluid inter-particle distance.
Those skilled in the art will appreciate that implementing all or part of the above described methods may be accomplished by way of a computer program stored on a non-transitory computer readable storage medium, which when executed, may comprise the steps of the embodiments of the methods described above. Any reference to memory, storage, database, or other medium used in the various embodiments provided herein may include non-volatile and/or volatile memory. The nonvolatile memory can include Read Only Memory (ROM), programmable ROM (PROM), electrically Programmable ROM (EPROM), electrically Erasable Programmable ROM (EEPROM), or flash memory. Volatile memory can include Random Access Memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms such as Static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double Data Rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous Link DRAM (SLDRAM), memory bus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), among others.
It will be apparent to those skilled in the art that, for convenience and brevity of description, only the above-described division of the functional units and modules is illustrated, and in practical application, the above-described functional distribution may be performed by different functional units and modules according to needs, i.e. the internal structure of the apparatus is divided into different functional units or modules to perform all or part of the above-described functions.
The above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention, and are intended to be included in the scope of the present invention.
Claims (7)
1. A numerical simulation method for a thin-walled structure, the method comprising:
step S1, determining a calculation domain according to the geometric dimension of a model file of a thin-wall structure, dividing the calculation domain into grids, determining a fixed wall boundary of the thin-wall structure, and determining a grid with a minimum distance Level-Set value meeting preset conditions from the grid to the fixed wall boundary; the Level-Set value of the solid wall boundary of the thin-wall structure is 0, and the ratio of the thickness of the solid wall boundary of the thin-wall structure to the size of the fluid particles is less than 4;
s2, calculating field variables which meet preset condition grids according to the Level-Set value;
s3, when the fluid particles are close to the fixed wall boundary, calculating the field variable of the fluid particles according to the field variable of the grid;
s4, supplementing the fluid particles close to the solid wall boundary with a momentum conservation equation and a missing item of the mass conservation equation through the physical properties and the field variables of the fluid particles to obtain the final acceleration and the density change rate of the fluid particles;
s5, performing time integration on the acceleration and the density change rate obtained by the calculation in the step S4 to obtain new fluid particle positions and fluid particle densities; if the Level-Set value of the new fluid particle position is smaller than a preset value, correcting the position and the speed of the fluid particle to obtain a corrected displacement field and a corrected speed field;
s6, repeating the steps S3-S5, so that the numerical simulation whole process solving of the thin-wall structure is completed;
step S2, according to the Level-Set value, calculating the field variables of each grid meeting the preset conditions, including:
if the field variable which accords with the preset condition grid is a unit normal vector, calculating the unit normal vector which accords with the preset condition grid through the following formula;
wherein,is the unit normal vector of the grid, +.>For the Level-Set value of the grid, +.>For Nabla operator, representing gradient;
if the field variable meeting the preset condition grid is a kernel function missing value and a kernel function gradient missing value, the field variable is obtained by the following smooth functionHComputing gridbFor the center grid meeting preset conditionscIs a contribution of (1):
wherein,is thatbThe temporary value of the number grid Level-Set is expressed as follows:
central grid meeting preset conditionscThe kernel missing values of (2) are:
central grid meeting preset conditionscThe kernel gradient missing values are:
wherein,Dthe dimensions of the problem are represented and,for nuclear function value->Gradient values for kernel functions;
step S4, through the physical properties and the field variables of the fluid particles, performing complement on the fluid particles close to the solid wall boundary by using a momentum conservation equation and a missing term of the mass conservation equation to obtain a final acceleration and a final density change rate of the fluid particles, including:
the final acceleration and density change rate of the fluid particles is calculated by the following formula:
wherein,for density change rate>For final acceleration +.>For the density of fluid particles a>For the pressure of fluid particles a>Is the velocity of fluid particle a; superscript-indicates that the entry is a boundary complement entry, < ->The value of the gradient absence of the kernel function in the field variable for the fluid particle a.
2. The method according to claim 1, wherein the step S1 of determining a calculation domain according to a geometric dimension of a model file of the thin-walled structure, performing mesh division on the calculation domain, determining a solid wall boundary of the thin-walled structure, and determining a mesh with a minimum distance Level-Set value from the mesh to the solid wall boundary meeting a preset condition includes:
importing a model file of the thin-wall structure, defining a geometric bounding box of the model according to the coordinate value range of the model file, and meshing the space in the bounding box;
calculating the Level-Set value of each grid, and enabling the Level-Set value to be smaller than or equal tokh + dxAnd a grid greater than or equal to 0 is determined as a grid meeting preset conditions, the grid is provided with a grid patternkIs the smooth length coefficient of the SPH method, thehIs of smooth radius, dxIs a mesh size.
3. The method according to claim 1, wherein step S3, when a fluid particle approaches the fixed wall boundary, calculates a field variable of the fluid particle from a field variable of the grid, comprises:
according to the coordinates of the fluid particles, acquiring indexes and direction weight values of grid center points around the fluid particles;
and calculating the field variable of the fluid particles through the field variable of the grid corresponding to the index of the central point of the surrounding grid and the direction weight value.
4. A method according to claim 3, wherein said calculating the field variable of the fluid particle from the field variable of the grid corresponding to the index of the surrounding grid center point and the direction weight value comprises:
when the problem is a three-dimensional problem, an index of grid center points around the fluid particles is obtainedi, j ,kAndWeight values in three directions；
For the field variable of the fluid particles, firstly, pairxInterpolation is carried out on the direction, and the following steps are obtained:
re-pairingyInterpolation is carried out on the direction to obtain:
finally tozInterpolation is carried out on the direction to obtain:
wherein,is the field variable of the fluid particle a, +.>、/>、/>、/>、/>、/>、/>、/>Corresponding field variables are indexed for 8 grid center points around the fluid particle a.
5. The method of claim 4, wherein the calculating the field variable of the fluid particle from the field variable of the grid corresponding to the index of the surrounding grid center point and the direction weight value comprises:
when the problem is a two-dimensional problem, an index of grid center points around the fluid particles is obtainedi, jWeight values in two directions；
For the field variable of the fluid particles, firstly, pairxInterpolation is carried out on the direction, and the following steps are obtained:
re-pairingyInterpolation is carried out on the direction to obtain:
wherein,for the field variation of the fluid particles a, < >>，/>，/>，/>Corresponding field variables are indexed for the 4 grid center points around the fluid particle.
6. The method according to claim 1, wherein the step S5 is to time integrate the acceleration and the density change rate calculated in the step S4 to obtain a new fluid particle position and a new fluid particle density; if the Level-Set value of the new fluid particle position is smaller than the preset value, correcting the position and the speed of the fluid particle to obtain a corrected displacement field and a corrected speed field, wherein the method comprises the following steps:
the position and velocity of the fluid particles are corrected by the following correction formula:
wherein, superscriptRepresenting the corrected value, ++>A displacement vector corrected for fluid particle a, +.>、/>Position and velocity before correction of fluid particles a, respectively, < >>、/>Respectively fluid particlesNormal vector of a and Level-Set value,/->Is the integration time step; />Is the fluid inter-particle distance.
7. A numerical simulation device suitable for use with a thin-walled structure, the device comprising:
the determining module is used for determining a calculation domain according to the geometric dimension of the model file of the thin-wall structure, dividing the calculation domain into grids, determining a fixed wall boundary of the thin-wall structure, and determining a grid with a minimum distance Level-Set value meeting preset conditions from the grid to the fixed wall boundary; the Level-Set value of the solid wall boundary of the thin-wall structure is 0, and the ratio of the thickness of the solid wall boundary of the thin-wall structure to the size of the fluid particles is less than 4;
the calculation module is used for calculating the field variables which accord with the preset condition grids according to the Level-Set value;
the calculation module is further used for calculating a field variable of the fluid particles according to the field variable of the grid when the fluid particles are close to the fixed wall boundary;
the calculation module is further used for supplementing the fluid particles close to the solid wall boundary with the loss terms of the momentum conservation equation and the mass conservation equation through the field variables of the fluid particles to obtain the final acceleration and the density change rate of the fluid particles;
the calculation module is also used for carrying out time integration on the acceleration and the density change rate obtained by calculation to obtain new fluid particle positions and fluid particle densities; if the Level-Set value of the new fluid particle position is smaller than a preset value, correcting the position and the speed of the fluid particle to obtain a corrected displacement field and a corrected speed field; completing the numerical simulation overall process solution of the thin-wall structure;
the computing module is specifically used for:
if the field variable which accords with the preset condition grid is a unit normal vector, calculating the unit normal vector which accords with the preset condition grid through the following formula;
wherein,is the unit normal vector of the grid, +.>For the Level-Set value of the grid, +.>For Nabla operator, representing gradient;
if the field variable meeting the preset condition grid is a kernel function missing value and a kernel function gradient missing value, the field variable is obtained by the following smooth functionHComputing gridbFor the center grid meeting preset conditionscIs a contribution of (1):
wherein,is thatbThe temporary value of the number grid Level-Set is expressed as follows:
central grid meeting preset conditionscThe kernel missing values of (2) are:
central grid meeting preset conditionscThe kernel gradient missing values are:
wherein,Dthe dimensions of the problem are represented and,for nuclear function value->Gradient values for kernel functions;
the final acceleration and density change rate of the fluid particles is calculated by the following formula:
wherein,for density change rate>For final acceleration +.>For the density of fluid particles a>For the pressure of fluid particles a>Is the velocity of fluid particle a; superscript-indicates that the entry is a boundary complement entry, < ->For nuclei in fluid particle a-field variablesFunction gradient missing values.
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