CN113408168B - High-precision numerical simulation method based on Riemann problem accurate solution - Google Patents
High-precision numerical simulation method based on Riemann problem accurate solution Download PDFInfo
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Abstract
The invention discloses a high-precision numerical simulation method based on Riemann problem accurate solving, and belongs to the field of multi-substance interaction high-precision numerical simulation. The invention combines a multi-substance arbitrary state equation Riemann problem accurate solving method and a virtual fluid method (GFM), and comprises a real virtual fluid method (RGFM), a wall surface virtual fluid method (WGFM), and a high-precision numerical simulation method which is simultaneously coupled with a weighted essentially non-oscillation (WENO) finite difference method and a Level-Set method (Level-Set). The invention can reduce the dissipation of shock waves and rarefaction waves in the process of propagation; the phenomenon of non-physical oscillation generated at the interface when the Euler equation is solved can be effectively inhibited, and the stable operation of the numerical value prediction process is guaranteed; the Riemann problem of any state equation can be solved accurately, the accurate interface state of multi-substance interaction is obtained, the accuracy of numerical calculation results in the multi-substance interaction process is improved, the prediction accuracy of the multi-substance interaction process is improved, and further the engineering technical problems related to the field of multi-substance interaction are solved.
Description
Technical Field
The invention relates to a high-precision numerical simulation method based on Riemann problem accurate solving, and belongs to the field of multi-substance interaction high-precision numerical simulation.
Background
The detonation of the explosive is accompanied by a violent chemical reaction that forms an explosive shock wave that propagates outward and produces a large amount of explosive gas product. The research on the propagation rule of the explosive shock waves has an important effect on preventing the explosive shock waves from damaging the structure.
The research on the explosive air explosion mainly comprises theoretical derivation, numerical simulation and experimental research. The theoretical derivation has certain guiding significance in early research, but the explosion has the characteristics of high temperature, high pressure, high speed and the like, is a typical complex nonlinear problem, causes great difficulty in theoretical derivation, simplifies the theoretical research, and generally has no universality and a narrow application range. The experimental study is the most direct and accurate study method, but the study period is long, the expenditure is high, the difficulty of carrying out the large equivalent prototype test is high, uncertain factors often exist in the test, the repeatability is poor, and the measurement and observation of the explosion test are also difficult.
With the development of computers, numerical simulation has become an important tool for studying explosion and impact problems. The numerical simulation has the advantages of perfect theory, high efficiency, strong adaptability, simple operation and the like, and compared with experimental research, the numerical simulation can greatly shorten the research period and reduce the research cost. The numerical simulation has the significance of replacing experiments to a certain extent, so that the experiment cost and the experiment risk are reduced, and meanwhile, the data with the error of the experiment result within a controllable range is obtained, and the precision of the numerical simulation result is very important. The existing numerical simulation technology usually adopts a virtual fluid method (GFM) and a method for solving a Riemannian problem to obtain an interface state combination when processing a multi-substance interaction problem, and the precision of the Riemannian problem solving directly influences the precision of the interface state, so that a numerical simulation result is greatly influenced. The Riemannian problem of the multi-substance complex state equation is generally solved by adopting an approximate solving method, the Riemannian problem of the multi-substance complex state equation is simplified into a double-wave structure by approximating the wave types, such as a double-shockwave approximate Riemannian problem solving method (TSRS), a double-sparse-wave Riemannian problem solving method (TRRS) and the like, an HLL method is obtained by derivation, and on the basis of the HLL multi-substance Riemannian solving method, consideration of contact discontinuity is added, and the HLLC method is obtained. Although the multi-substance Riemann problem solving method has wide application, the method fails to judge the type of the wave generated by the interaction of the multi-substance, is an approximate Riemann solving method, has large solving error, causes low interface state precision and further causes reduction of numerical simulation result precision, and needs to be made up urgently, so that the method has important engineering value and application significance.
Disclosure of Invention
Aiming at the problems that the Riemann problem in the existing multi-substance interaction numerical simulation method is solved by an approximation method, the interface state error is large, the calculation result precision is influenced and the like, the invention discloses a multi-substance interaction high-precision numerical simulation method based on the Riemann problem precision solving, which aims to solve the technical problems that: the Riemann problem of any state equation is solved accurately, the accurate interface state of the multi-substance interaction is obtained, the accuracy of the numerical calculation result of the multi-substance interaction process is improved, the prediction accuracy of the multi-substance interaction process is improved, and the engineering technical problem related to the field of the multi-substance interaction is solved.
The fields of multi-material interaction comprise high-speed/ultra-high-speed warhead penetration and protection, explosion and structure interaction, aerospace and mechanical engineering fields.
The purpose of the invention is realized by the following technical scheme.
The invention discloses a high-precision numerical simulation method based on Riemann problem accurate solving, which is a high-precision numerical simulation method combining a multi-substance arbitrary state equation Riemann problem accurate solving method and a virtual fluid method (GFM), and comprises a real virtual fluid method (RGFM), a wall surface virtual fluid method (WGFM), and a high-precision numerical simulation method simultaneously coupled with a weighted essential shock-free (WENO) finite difference method and a Level-Set method (Level-Set), so that the precision of interface state solving can be improved, and the errors of numerical simulation results and experimental results can be reduced. The WENO finite difference format converts flux solution in an Euler equation into high-precision discrete solution by selecting lattice points of a spatial template, so that numerical value oscillation is reduced while precision is ensured; the Level-Set method can effectively track the position change of the complex multi-medium interface; the RGFM method processes the interface state by setting a virtual flow field, and keeps the pressure and speed continuity of the interface; the WGFM method realizes the multi-substance coupling numerical simulation of the fluid and the rigid body by setting a virtual wall surface interface state at the interface of the fluid and the rigid body; the method for accurately solving the Riemann problem of the multi-substance arbitrary state equation can obtain the accurate interface state of the interaction of the multi-substance by accurately solving the Riemann problem of the arbitrary state equation, and improves the numerical simulation precision. The invention can effectively realize high-precision numerical solution on the problem of multi-substance interaction.
The invention discloses a high-precision numerical simulation method based on Riemann problem accurate solving, which realizes multi-substance interaction high-precision numerical simulation based on Riemann problem accurate solving and comprises the following steps:
step 1: determining a calculation region according to an actual problem, establishing an Euler rectangular coordinate system, dividing the x direction of the calculation region into m grids, dividing the y direction into n grids, dividing the z direction into l grids, and counting m × n × l grids.
And 2, step: defining a level set level-set function in the calculation area for distinguishing the initial state interface position of each substance, defining the initial physical quantity, the material state equation and the conservation type Euler control equation set of each substance according to the area divided by the level-set, and simultaneously setting boundary conditions.
The conservation-oriented Euler control equation system is as follows:
wherein the content of the first and second substances,
e is the total energy of unit mass of the material, E is the specific internal energy of the material,
g is the gravitational acceleration, u, v, w are the velocities in the x, y, z directions, respectively, p is the pressure of the material, ρ is the density of the material.
And step 3: and taking a calculation parameter CFL to calculate the time step.
And 4, step 4: solving the normal vector of the material interface in each area, and establishing a Riemann problem along the normal direction of the material interface according to the properties of the materials on two sides of the interface.
And 5: and (3) accurately solving a method MERS by using a multi-substance Riemann problem to obtain a physical state after the substances on two sides of the interface interact.
Step 5.1: along the normal direction, L and R denote the substances on both sides of the interface, and L and R denote the substances on both sides of the interface after the interaction, respectively.
And step 5.2: according to the physical state of the substances on the two sides of the interface, the speed of the wave generated by the interaction of the substances on the two sides of the interface and the interface speed are preliminarily calculated, and the formula is as follows:
wherein s is L 、s R Respectively the velocity of the two side waves, s c Is the interface velocity, u L 、u R Respectively the velocity of the two side materials, p L 、ρ R Density of bilateral substances, p L 、p R The pressures of the two side materials are respectively.
Step 5.3: and (3) preliminarily calculating the physical state of the two sides of the interface after the substances interact according to the wave velocity obtained in the step 5.2 by utilizing the R-H relation of the shock wave, wherein the general formula is as follows:
where ρ is L* 、ρ R* Respectively the density of the substances on both sides of the interface after interaction, u L* 、u R* Respectively the velocities of the substances on both sides of the interface after interaction, E L* 、E R* Respectively, specific energy of substances on both sides of the interface after interaction, p L* 、p R* Respectively, the pressure of the substances on both sides of the interface after interaction, E L 、E R The specific energy of the two side materials is respectively.
Step 5.4: and judging the types of waves generated by the interaction of substances on two sides of the interface according to the entropy condition, wherein the types comprise shock waves and rarefaction waves.
And step 5.5: according to the judgment of the wave types at the two sides in the step 5.4, different calculation methods are adopted according to different wave types to obtain the wave velocity s corresponding to the wave velocity L 、s R The precise physical state of the material on both sides of the interface after interaction.
Step 5.5a: for shock wave, the relation of R-H of shock wave is used to solve the wave speed s L Or s R The physical state of the single side after the interaction of the substances on both sides of the interface.
Step 5.5a said solving out wave velocity s L Or s R The method for the physical state of the single side after the interaction of the substances on the two sides of the interface comprises the following steps: adopting a Newton iteration method, wherein the formula is as follows:
Or
U L 、U R Respectively, the conservation variables of the two side substances, U L* 、U R* As a conservation variable of the substances on both sides of the interface after interaction, F L 、F R Respectively, the conservation variables of the two side substances, F L* 、F R* Is the conservation variable of substances on two sides of the interface after interaction, and further obtains the wave velocity s L Or s R The physical state of the single side after the interaction of the substances on both sides of the interface.
Step 5.5b: for sparse waves, the wave velocity s is obtained by utilizing the relation of sparse waves L Or s R The physical state of the single side after the interaction of the substances on both sides of the interface.
The specific implementation method of the step 5.5b is as follows:
wherein u is L -c L ≤ξ≤u L* -c L* Or u R +c R ≤ξ≤u R* +c R*
Obtaining a wave velocity of s L Or s R The physical state of the single side after the interaction of the substances on both sides of the interface.
Step 5.6: and (5) correcting the speed of the wave generated by the interaction of the substances on the two sides of the interface according to the physical state obtained in the step (5.5) after the interaction of the substances on the two sides of the interface.
The specific implementation method of the step 5.6 comprises the following steps: newton iteration is adopted, and the formula is as follows:
wherein the content of the first and second substances,
calculating by adopting a perturbation method:
step 5.7: and (5.5) repeating the step 5.5-5.6 until the precision requirement is met, and obtaining the precise wave velocity and the interface speed of the wave generated by the interaction of the substances on the two sides of the interface and the precise physical state of the interacted substances on the two sides of the interface corresponding to the precise wave velocity.
Step 6: and obtaining the physical state of the grid near the multi-substance interaction interface by adopting different GFM methods according to different properties of substances on two sides of the interface.
Adopting an RGFM method aiming at the interaction between the fluid and adopting a WGFM method aiming at the interaction between the fluid and the rigid body; and then determining the physical state of the multilayer grid near each material interface according to the precise physical state obtained in the step 5 after the materials on the two sides of the interface interact, and calculating other materials in the same way to obtain the physical state of the multilayer grid near each material interface.
And 7: respectively carrying out space dispersion and time dispersion on the calculation area of each substance by adopting a high-precision finite difference WENO format and a TVD Runge-Kutta format to obtain t n+1 The physical state of each material region at that time.
And 8: a level-set function is advanced to obtain t n+1 Level-Set function of each material region at time, i.e. t n+1 The position of the interface of each substance at the moment.
And step 9: t obtained according to step 8 n+1 At the moment, the position of each material interface is determined, and t is obtained in the step 7 n+1 Integrating the physical states of the material areas at the moment to obtain t n+1 The physical state of the entire computing area at the moment.
Step 10: judging the current calculation time t n+1 Whether the set end time t is exceeded end If t is n+1 ＞t end If so, ending the numerical calculation and outputting the physical state of the whole calculation area at the moment; if t is n+1 ＜t end And returning to the step 3, and continuing to perform the multi-substance interaction high-precision numerical simulation.
Further comprising the step 11: the Riemann-based problem accurate solving is carried out by utilizing the steps 1 to 10, the high-precision numerical simulation of the multi-substance interaction is realized, the precision of the numerical simulation of the multi-substance interaction process is improved, the goodness of fit with an experimental result is improved, the prediction precision of the multi-substance interaction process can be improved, and further the related engineering technical problem in the field of the multi-substance interaction is solved.
The fields of multi-substance interaction comprise high-speed/ultra-high-speed penetration and protection, aerospace navigation and mechanical engineering fields.
Predicting a multi-substance interaction process in the engineering field, wherein the multi-substance interaction process comprises explosive air explosion, near-ground explosion, deep water explosion, water surface explosion, energy-gathering jet flow, ultra-high speed collision problem, supernova explosion and Rayleigh Taylor instability problem.
Has the advantages that:
1. the high-precision numerical value simulation method based on the Riemann problem accurate solution can improve the precision of numerical calculation results in the multi-substance interaction process, improve the goodness of fit with experimental results, and further accurately predict the multi-substance interaction problems in the engineering field such as explosive air explosion, near-ground explosion, deep water explosion, water surface explosion, energy-gathering jet flow, ultra-high speed collision problem, supernova explosion, rayleigh Taylor instability problem and the like.
2. The invention discloses a high-precision numerical simulation method based on Riemann problem accurate solution, which is characterized in that a WENO format is adopted to disperse a space derivative term of an Euler equation, and a TVD Runge-Kutta format is adopted to disperse a time derivative term of the Euler equation.
3. The invention discloses a high-precision numerical simulation method based on Riemann problem accurate solution, which adopts a multi-substance arbitrary state equation Riemann problem accurate solution method combined with RGFM and WGFM methods according to different substance properties at two sides of an interface to process the strong discontinuity problem of multi-substance interface interaction and has the discontinuity characteristic of high resolution of a substance interface; compared with the classical GFM method, the method can effectively process various complex state equations, can effectively improve the precision of processing the interaction of multiple substances, can effectively inhibit the non-physical oscillation phenomenon generated at the interface when the Euler equation is solved, and can ensure the stable operation of the numerical simulation process.
4. The invention discloses a high-precision numerical simulation method based on Riemann problem accurate solution, which adopts a Riemann problem accurate solution method of a multi-substance arbitrary state equation, can accurately process various complex state equations compared with the traditional multi-substance approximate Riemann solution method, can obtain accurate physical states of substances on two sides of a multi-substance interaction interface, improves the accuracy of multi-substance interaction calculation, reduces errors with experimental results, and has obvious advantages in processing the multi-substance complex state equation interaction problem in the engineering field.
Drawings
FIG. 1 is a structural diagram of a Riemannian problem and a wave system, wherein a is a schematic diagram of the Riemannian problem, and b is a schematic diagram of the wave system structure of the Riemannian problem;
FIG. 2 is a schematic diagram of entropy conditional decision wave types;
FIG. 3 is a schematic diagram of precision Riemann's solution in conjunction with RGFM;
FIG. 4 is a schematic diagram of precision Riemann's solution in conjunction with WGFM;
FIG. 5 is a schematic view of an initial geometric model of example 1;
FIG. 6 is a blast protected structure of example 1;
FIG. 7 is a schematic view of the explosion shock wave pressure monitoring points in example 1;
FIG. 8 is a pressure contour plot at different times of the detonation flow field of example 1;
FIG. 9 is a cloud of numerically simulated pressures for interaction of the blast shock wave with the containment structure of example 1;
FIG. 10 is a comparison of the numerical simulation of the explosion shock wave pressure monitoring points and the test pressure curves of example 1;
fig. 11 is a flowchart of an embodiment 1 disclosing a high-precision numerical simulation method for multi-substance interaction based on the riemann problem accurate solution.
Detailed Description
Example 1:
for better illustrating the objects and advantages of the present invention, the present invention will be further described with reference to the accompanying drawings and examples.
The present embodiment finds application in the example of the interaction of an explosive blast with a protective structure.
The initial geometric model in the calculation example disclosed in the embodiment is shown in the attached drawing (5), the shock wave protection structure and the pressure monitoring points are respectively shown in the attached drawings (6) and (7), the pressure isosurface maps of different moments of the explosion flow field are shown in the attached drawing (8), the numerical simulation pressure cloud map of the interaction between the explosion shock wave and the protection structure is shown in the attached drawing (9), and the comparison of the numerical simulation and the test shock wave pressure curve is shown in the attached drawing (10).
As shown in fig. 11, the embodiment discloses a high-precision numerical simulation method based on the precision solving of the riemann problem, which includes:
step 1: according to the actual physical problem, a calculation region is determined to be 58m 22m 1m, an Euler rectangular coordinate system is established, the x direction of the calculation region is divided into 696 grids, the y direction is divided into 264 grids, the z direction is divided into 132 grids, and 24254208 grids are counted.
Step 2: as shown in attached drawings (5) and (6), the overall span and height of the protective structure are respectively 13m and 6.8m, the thickness of the main wall structure is 0.3m, the length of the main wall structure is 9m, the height of the main wall structure is 6.8m, the height of the supporting structure is 0.25m, the length of the supporting structure is 0.9m, the wing wall structure is L-shaped and is the same as the thickness and height of the main wall, the length of the wing wall structure is 2m, the length of a part of the wing wall perpendicular to the main wall surface is 1.05m, 1t TNT explosive is arranged at a position 45m away from the main wall surface, and according to the defined level-set function, the calculation area is divided into air, explosive and the protective structure. The values of the initial states of the air and the explosive and the parameters of the state equation are shown in the following table:
table 1:
according to the practical physical problem, a non-reflection boundary condition is set at the boundary so as to realize an infinite air domain.
And step 3: the CFL parameter takes 0.3 and calculates the time step.
Step 4, solving the normal vector of the material interface in each area by using a level-set function, wherein the solving formula is as follows:
and 4.2: and according to the normal vector of the material interface and the properties of the materials on two sides of the interface, establishing the Riemann problem between the materials on two sides of the interface along the normal direction of the material interface.
Aiming at the interaction between the fluid and the fluid, a Riemann problem is established according to different physical states of the fluid on two sides of the interface along the normal direction of the interface; aiming at the interaction between the fluid and the solid, a wall Riemann problem is established according to the physical state of the fluid on one side of the interface along the normal direction of the interface.
And 5: solving the Riemann problem in the normal direction established in the step 4, firstly, preliminarily calculating the speed of the wave generated by the interaction of the substances on the two sides of the interface and the interface speed, and preliminarily calculating the physical state of the substances on the two sides of the interface after the interaction by utilizing the R-H relation of the shock wave; secondly, accurately judging the types of waves on two sides of the interface according to entropy conditions; then different calculation methods are adopted according to different wave types on two sides of the interface, for shock waves, a shock wave R-H relational expression and a Newton iteration method are combined, for sparse waves, a sparse wave relation and a classical 4-order Runge Kutta method are combined, and a physical state after interaction of substances on two sides of the interface corresponding to the wave speed obtained through preliminary calculation is obtained; then, according to the contact interruption condition, newton iteration is adopted to correct the wave speeds of the two sides of the interface; and finally, repeating the process until the precision requirement is met, and obtaining the precise speed of the wave generated by the interaction of the substances on the two sides of the interface, the interface speed and the precise physical state of the interacted substances on the two sides of the interface corresponding to the precise wave speed.
Step 6: and obtaining the physical state of the grid near the multi-substance interaction interface by adopting different GFM methods according to different properties of substances on two sides of the interface.
Adopting an RGFM method aiming at the interaction between the fluid and the fluid, adopting a WGFM method aiming at the interaction between the fluid and the rigid body, and then determining the physical state of the multilayer grid near each material interface according to the precise physical state obtained in the step 5 after the materials on the two sides of the interface interact, wherein the method comprises the following specific steps:
when the material 1 is calculated, setting the calculation area of other materials as a virtual grid, wherein the information on the virtual grid is obtained by extending the accurate physical state after the interaction of the materials on the two sides of the interface obtained in the step 5, and the extension equation is as follows:
wherein, I represents physical quantities such as density, speed, pressure and the like, and n is a gradient direction vector of the point. The physical state of the multi-layer lattice in the vicinity of the interface of the substance 1 is thus obtained. And calculating other substances in the same way to obtain the physical state of the multilayer grid near each substance interface.
And 7: respectively carrying out space dispersion and time dispersion on the calculation region of each substance by adopting a high-precision finite difference WENO format and a TVD Runge-Kutta format to obtain t n+1 The physical state of each material region at that time.
Step 7.1: preferably, a 5 th-order WENO format is adopted to discretize the spatial derivative term in the conservation-oriented Euler control equation set in the step 2.3, so as to obtain an ordinary differential equation set of the conservation variable relative to the time derivative:
step 7.2: preferably, the third-order TVD change-Kutta format is adopted to discretize the time derivative term of formula (14), the term at the right end of the equation (11) with the equal sign is denoted as L, and the propulsion time step is Δ t, so as to obtain the fully discrete format of the conservation-oriented euler control equation set:
step 7.3: repeating the steps 7.1-7.2, and performing space dispersion and time dispersion on the calculation region of each substance to obtain t n+1 The physical state of each material region at the time.
And step 8: respectively dispersing a spatial derivative term and a time derivative term of the Level-Set motion equation by adopting an HJ-WENO format and a TVD Runge-Kutta format to obtain a full dispersion format of the Level-Set motion equation,
and then get t n+1 The Level-Set function of each material area at the moment.
And step 9: t obtained according to step 8 n+1 At the moment, the position of each material interface is determined, and t obtained in the step 7 is compared with t n+1 Integrating the physical states of the material areas at the moment to obtain t n+1 The physical state of the entire computing area at the moment.
And then, carrying out steps 10 to 11 to obtain a numerical simulation result of the interaction between the explosive blast wave and the protective structure.
And (4) analysis of calculation results:
the attached figure (8) is a pressure isosurface map of an explosion flow field at different moments, and it can be known from the figure that after an explosive explodes, explosion shock waves are transmitted in the air, after the explosion shock waves reach a protection structure, part of the explosion shock waves form reflection shock waves due to reflection of a main wall surface, and part of the explosion shock waves are influenced by reflection and diffraction of a wing wall structure. The attached drawing (9) is a pressure cloud chart of interaction between the explosion shock wave and the protective structure, and the reflection and diffraction of the explosion shock wave by the wing wall structure can be more obviously seen from the cloud chart, moreover, the Mach reflected wave formed by the explosion shock wave after reflection and diffraction on the wall surface can be seen in the area A, and the explosion shock wave transmitted through a communication structure such as a window can be seen in the area B. The figure (10) is a comparison of numerical simulation of the explosion shock wave pressure monitoring point and a test pressure curve, the comparison of the numerical simulation and the test result shows that the pressure curve has small peak value error and approximate overall trend, and the accuracy and the effectiveness of the numerical simulation technology are proved.
The above detailed description is further intended to illustrate the objects, technical solutions and advantages of the present invention, and it should be understood that the above detailed description is only an example of the present invention and should not be used to limit the scope of the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (8)
1. A high-precision numerical simulation method based on Riemann problem accurate solution is characterized by comprising the following steps: the method is used for realizing high-precision numerical simulation of interaction of various substances such as gas, explosive, water, metal and rigid bodies based on Riemann problem accurate solution, and comprises the following steps:
step 1: determining a calculation region according to an actual problem, establishing an Euler rectangular coordinate system, dividing the x direction of the calculation region into m grids, dividing the y direction into n grids, dividing the z direction into l grids, and counting m × n × l grids;
and 2, step: defining a level set level-set function in a calculation area, distinguishing initial interface positions of all substances, defining initial physical quantities, material state equations and conservation type Euler control equation sets of all the substances according to different substances divided by the level-set, and simultaneously setting boundary conditions;
the conservation-oriented Euler control equation system is as follows:
wherein, the first and the second end of the pipe are connected with each other,
e is the total energy of unit mass of the material, E is the specific internal energy of the material,
g is the gravity acceleration, u, v and w are the speeds in the directions of x, y and z respectively, p is the pressure of the substance, and rho is the density of the substance;
and 3, step 3: calculating the time step length by taking the calculated parameter convergence condition judgment number CFL;
and 4, step 4: solving the normal vector of each material interface, and establishing a Riemann problem along the normal direction of the material interface according to the physical states of the materials on the two sides of the interface;
and 5: accurately solving a method MERS by utilizing a multi-substance Riemann problem to obtain a physical state after substances on two sides of an interface interact;
step 6: according to different properties of substances on two sides of the interface, adopting different virtual fluid methods GFM to obtain the physical state of a grid near the multi-substance interaction interface;
and 7: respectively carrying out space dispersion and time dispersion on a calculation area where each substance is positioned by adopting a high-precision finite difference WENO format and a TVD Runge-Kutta format to obtain t n+1 The physical state of each substance at the moment;
and step 8: advancing the level-set function to obtain t n+1 Level-Set function of each material region at time, i.e. t n+1 The position of each material interface at the moment;
and step 9: t obtained according to step 8 n+1 At the moment, the position of each material interface is determined, and t is obtained in the step 7 n+1 Integrating the physical states of all the substances at the moment to obtain t n+1 The physical state of the whole calculation area at any moment;
step 10: judging the current calculation time t n+1 Whether the set end time t is exceeded or not end If t is n+1 ＞t end If so, ending the numerical calculation and outputting the physical state of the whole calculation area at the moment; if t is n+1 ＜t end And returning to the step 3, and continuing to carry out the high-precision numerical simulation of the multi-substance interaction.
2. The high-precision numerical simulation method based on the Riemann problem accurate solution according to claim 1, wherein: the fields of multi-substance interaction comprise high-speed/ultrahigh-speed penetration and protection, aerospace navigation and mechanical engineering fields.
3. The high-precision numerical simulation method based on the Riemann problem accurate solution as claimed in claim 2, wherein: predicting a multi-material interaction process in the engineering field, wherein the multi-material interaction process comprises explosive air explosion, near-ground explosion, deep water explosion, water surface explosion, energy-gathering jet flow, ultra-high speed collision problem, supernova explosion and Rayleigh Taylor instability problem.
4. A high accuracy numerical simulation method based on the precision solving of the riemann problem as claimed in claim 1, 2 or 3 wherein: the step 5 is realized by the method that,
step 5.1: along the normal direction, respectively representing substances on two sides of the interface by L and R, and respectively representing substances on two sides of the interface after interaction by L and R;
step 5.2: according to the physical state of the substances on the two sides of the interface, the speed of the wave generated by the interaction of the substances on the two sides of the interface and the interface speed are preliminarily calculated, and the formula is as follows:
wherein s is L 、s R Respectively the velocity of the two side waves, s c Is the interface velocity, u L 、u R Respectively the velocity of the two side substances, p L 、ρ R Density of bilateral substances, p L 、p R Respectively the pressure of the substances on both sides;
step 5.3: and (3) preliminarily calculating the physical state of the two sides of the interface after the substances interact according to the wave velocity obtained in the step 5.2 by utilizing the R-H relation of the shock wave, wherein the general formula is as follows:
where ρ is L* 、ρ R* The densities u of the substances on both sides of the interface after the interaction L* 、u R* Respectively the velocities of the substances on both sides of the interface after interaction, E L* 、E R* Respectively, the specific energy of the substances on both sides of the interface after the interaction, p L* 、p R* Respectively, the pressure of the substances on both sides of the interface after interaction, E L 、E R Specific energy of the two side substances, c L 、c R The sound velocities of the substances on both sides are respectively;
step 5.4: judging the types of waves generated by the interaction of substances on two sides of the interface according to the entropy condition, wherein the types comprise shock waves and rarefaction waves;
step 5.5: according to the judgment of the wave types at the two sides in the step 5.4, different calculation methods are adopted according to different wave types to obtain the wave velocity s corresponding to the wave velocity L 、s R The substances on the two sides of the interface are in an accurate physical state after interaction;
step 5.5a: for shock wave, the relation of R-H of shock wave is used to solve the wave speed s L Or s R The physical state of one side after the interaction of substances on the two sides of the interface;
step 5.5b: for sparse waves, the wave velocity s is obtained by utilizing the relation of sparse waves L Or s R The physical state of one side after the interaction of substances on the two sides of the interface;
step 5.6: correcting the speed of the wave generated by the interaction of the substances on the two sides of the interface according to the physical state obtained in the step 5.5 after the substances on the two sides of the interface interact with each other;
step 5.7: and (5.5) repeating the steps 5.5-5.6 until the precision requirement is met, and obtaining the precise wave velocity and the interface speed of the wave generated by the interaction of the substances on the two sides of the interface and the precise physical state of the substances on the two sides of the interface corresponding to the precise wave velocity after the interaction.
5. The high-precision numerical simulation method based on the Riemann problem accurate solution as claimed in claim 4, wherein: step 5.5a solving for the wave velocity s L Or s R The method for the physical state of one side after the interaction of substances on two sides of the interface comprises the following steps: the Newton iteration method is adopted, and the formula is as follows,
wherein R is s ＝F L -F L* -s L (U L -U L* ) Or R s ＝F R -F R* -s R (U R -U R* )
Or
U L 、U R Are respectively the conservation variables of the substances on both sides, U L* 、U R* The conservation variable of the substances on both sides of the interface after interaction, F L 、F R Respectively, the conservation variables of the two side substances, F L* 、F R* Is the conservation variable of substances on two sides of the interface after interaction, and then the wave velocity is s L Or s R Physical state of one side after interaction of substances on both sides of the interface, W L 、W R Respectively representing the original variables of the two side substances, lambda (W) L )、λ(W R ) Respectively represent the characteristic values of substances on both sides, r (W) L )、r(W R ) Respectively, corresponding to the characteristic value lambda (W) L )、λ(W R ) Characteristic vector of (xi) L 、ξ R Respectively represent the sparse wave velocity intervals of the substances on both sides, c L 、c R Respectively the sound velocity of the two-sided material, c L* 、c R* Respectively the sound velocity of the substances on two sides of the interface after the interaction to obtain the wave velocity s L Or s R The physical state of one side after interaction of substances on both sides of the interface.
6. The high-precision numerical simulation method based on the Riemannian problem accurate solution according to claim 5, wherein: the specific implementation of step 5.5b is,
wherein u is L -c L ≤ξ≤u L* -c L* Or u R +c R ≤ξ≤u R* +c R*
Obtaining a wave velocity of s L Or s R The physical state of one side after interaction of substances on both sides of the interface.
7. The high-precision numerical simulation method based on the Riemann problem accurate solution according to claim 6, wherein: the specific implementation method of the step 5.6 comprises the following steps: newton iteration is adopted, and the formula is as follows,
wherein, the first and the second end of the pipe are connected with each other,
calculating by adopting a perturbation method:
8. the high-precision numerical simulation method based on the Riemann problem accurate solution according to claim 7, wherein: the step 6 is realized by the method that,
adopting a real virtual fluid method RGFM aiming at the interaction between the fluid and the fluid, and adopting a wall virtual fluid method WGFM aiming at the interaction between the fluid and the rigid body; and then determining the physical state of the multilayer grid near each material interface according to the precise physical state obtained in the step 5 after the materials on the two sides of the interface interact, and calculating other materials in the same way to obtain the physical state of the multilayer grid near each material interface.
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