CN116882322B - Calculation method and device for non-sticky flux, terminal equipment and storage medium - Google Patents
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Abstract
The application discloses a calculation method, a device, terminal equipment and a storage medium of non-sticky flux, wherein a grid unit to be calculated is obtained, and solution points and flux points of the grid unit are determined according to the grid unit; determining physical information corresponding to flux points according to preset initial conditions; calculating non-sticky flux corresponding to the flux points according to the physical information corresponding to the flux points and a preset split form; according to the non-sticky flux corresponding to the flux point, determining a first derivative of the non-sticky flux in a conservation form at the solving point and a first derivative of the non-sticky flux in a non-conservation form at the solving point; determining flux information at interfaces of grid cells, and determining correction information of non-sticky flux in a conservation form; and further determining discrete terms of the non-stick flux of the grid cells to be calculated; and the target non-sticky flux of the grid unit to be calculated is determined, so that the calculation stability is improved, and the discrete conservation law is satisfied.
Description
Technical Field
The application belongs to the technical field of fluid mechanics, and particularly relates to a calculation method, a device, terminal equipment and a storage medium of non-sticky flux.
Background
Computational fluid dynamics (Computational Fluid Dynamics, CFD) is a supplement to theory and experiment by numerical methods to study hydrodynamic problems. In recent years, with the increasing requirement of fine simulation of flow problems, a high-order format becomes an important research direction in the field of CFD because of the characteristics of small numerical dissipation error and dispersion error. At a certain computation time, higher order formats have lower numerical dissipation than lower order formats. The reconstruction correction process (Correction Procedure via Reconstruction: CPR) method can be restored to the existing high-order methods, such as Discontinuous Galerkin (DG) method, spectrum difference (Spectral Difference: SD) method, etc., by adjusting the correction function, and the method has small calculation amount and low calculation complexity, can be applied to unstructured grids and complex boundaries, and has recently received attention from many researchers.
For higher order spectral/finite element-like methods like the CPR method, they all construct a numerical solution within each grid cell using a finite set of basis functions. When such methods are applied to nonlinear equations, errors can occur if any of the modes generated by the nonlinear term is outside the range of the set of basis functions.
In these cases, energy from the under-resolved mode is aliased onto the lower mode, creating a so-called aliasing error. The impact of aliasing errors on a given simulation is unpredictable and is prone to severe instability. In order to enhance the stability of the under-resolved flow simulation, a defrobulation technique, such as a split form, is required, and although the stability of the compressible turbulence simulation can be enhanced, the discrete conservation rate cannot be satisfied, and how to enhance the stability of the multi-scale structure can be enhanced, and the discrete conservation rate can also be satisfied, which is a problem that is continuously solved at present.
Disclosure of Invention
The application aims to provide a calculation method, a device, terminal equipment and a storage medium without sticky flux, so as to solve the defects in the prior art, and the technical problem to be solved by the application is realized through the following technical scheme.
In a first aspect, embodiments of the present application provide a method for calculating a non-stick flux, the method including:
obtaining a grid cell to be calculated, and determining flux points of the grid cell according to the grid cell;
determining physical information corresponding to flux points according to preset initial conditions;
calculating the non-sticky flux corresponding to the flux point according to the physical information corresponding to the flux point and a preset split form, wherein the non-sticky flux at least comprises the non-sticky flux in a conservation form and the non-sticky flux in a non-conservation form;
According to the non-sticky flux corresponding to the flux point, determining a first derivative of the non-sticky flux in a conservation form at the solving point and a first derivative of the non-sticky flux in a non-conservation form at the solving point;
determining flux information at interfaces of the grid cells, and determining correction information of non-sticky flux in a conservation form;
determining a discrete item of the non-sticky flux of the grid unit to be calculated according to the first derivative of the non-sticky flux in the conservation form at the solving point, the first derivative of the non-sticky flux in the non-conservation form at the solving point and the correction information of the non-sticky flux in the conservation form;
and determining the target non-stick flux of the grid unit to be calculated according to the discrete items of the non-stick flux of the grid unit to be calculated.
Optionally, the calculating the non-sticky flux corresponding to the flux point according to the physical information corresponding to the flux point and a preset split form includes:
according to a preset splitting form, splitting the non-sticky flux corresponding to the flux point into a combination of the non-sticky flux in a conservation form and the non-sticky flux in a non-conservation form, wherein the non-sticky flux in the combination is split into a combination coefficient of the non-sticky flux in the conservation form and the non-sticky flux in the non-conservation form, and the combination coefficient is different.
Optionally, the solution points are gaussian points, and the solution points and the flux points are staggered.
Optionally, the determining physical information corresponding to the flux point according to the preset initial condition includes:
calculating physical information corresponding to the solving point according to the preset initial conditions, wherein the preset initial conditions at least comprise flow field initial conditions, and the physical information at least comprises one or more of density, pressure and speed;
and constructing a Lagrange interpolation polynomial at the solving point to obtain physical information corresponding to the flux point.
Optionally, the determining the first derivative of the non-stick flux in the conservation form at the solving point and the first derivative of the non-stick flux in the non-conservation form at the solving point according to the non-stick flux corresponding to the flux point includes:
determining a first derivative of the non-stick flux in the conservation form at the solution point according to the non-stick flux in the conservation form at the flux point;
determining a first derivative of the non-stick flux in the non-conservative form at the solution point from the non-stick flux in the non-conservative form at the flux point.
Optionally, the determining flux information at the interface of the grid cell, determining correction information of non-stick flux in conservation form, includes:
Calculating the Riemann flux at the interface of the grid cells and the non-sticking flux at the interface;
and obtaining correction information of the non-sticky flux in a conservation form according to the left and right correction functions of the flux points at the interfaces.
In a second aspect, embodiments of the present application provide a non-stick flux computing device, the device comprising:
the acquisition module is used for acquiring the grid cells to be calculated and determining flux points of the grid cells according to the grid cells;
the first determining module is used for determining physical information corresponding to the flux points according to preset initial conditions;
the second determining module is used for calculating the non-sticky flux corresponding to the flux point according to the physical information corresponding to the flux point and a preset split form, wherein the non-sticky flux at least comprises the non-sticky flux in a conservation form and the non-sticky flux in a non-conservation form;
the third determining module is used for determining a first derivative of the non-sticky flux in a conservation form at the solving point and a first derivative of the non-sticky flux in a non-conservation form at the solving point according to the non-sticky flux corresponding to the flux point;
a fourth determining module, configured to determine flux information at interfaces of the grid cells, and determine correction information of non-sticky flux in a conservation form;
The correction module is used for determining the discrete items of the non-sticky flux of the grid unit to be calculated according to the first derivative of the non-sticky flux in the conservation form at the solving point, the first derivative of the non-sticky flux in the non-conservation form at the solving point and the correction information of the non-sticky flux in the conservation form;
and a fifth determining module, configured to determine a target non-stick flux of the grid unit to be calculated according to the discrete term of the non-stick flux of the grid unit to be calculated.
Optionally, the second determining module is configured to:
according to a preset splitting form, splitting the non-sticky flux corresponding to the flux point into a combination of the non-sticky flux in a conservation form and the non-sticky flux in a non-conservation form, wherein the non-sticky flux in the combination is split into a combination coefficient of the non-sticky flux in the conservation form and the non-sticky flux in the non-conservation form, and the combination coefficient is different.
Optionally, the solution points are gaussian points, and the solution points and the flux points are staggered.
Optionally, the first determining module is configured to:
calculating physical information corresponding to the solving point according to the preset initial conditions, wherein the preset initial conditions at least comprise flow field initial conditions, and the physical information at least comprises one or more of density, pressure and speed;
And constructing a Lagrange interpolation polynomial at the solving point to obtain physical information corresponding to the flux point.
Optionally, the third determining module is configured to:
determining a first derivative of the non-stick flux in the conservation form at the solution point according to the non-stick flux in the conservation form at the flux point;
determining a first derivative of the non-stick flux in the non-conservative form at the solution point from the non-stick flux in the non-conservative form at the flux point.
Optionally, the correction module is configured to:
calculating a Riemann flux at the interface of the grid cells and a non-stick flux at the interface;
and obtaining correction information of the non-sticky flux in a conservation form according to the left and right correction functions of the flux points at the interfaces.
In a third aspect, an embodiment of the present application provides a terminal device, including: at least one processor and memory;
the memory stores a computer program; the at least one processor executes the computer program stored by the memory to implement the non-stick flux calculation method provided in the first aspect.
In a fourth aspect, embodiments of the present application provide a computer readable storage medium having a computer program stored therein, the computer program when executed implementing the non-stick flux calculation method provided in the first aspect.
Embodiments of the present application include the following advantages:
according to the non-sticky flux calculating method, the non-sticky flux calculating device, the terminal equipment and the storage medium, the grid cells to be calculated are obtained, and flux points of the grid cells are determined according to the grid cells; determining physical information corresponding to flux points according to preset initial conditions; according to the physical information corresponding to the flux points and a preset split form, calculating the non-sticky flux corresponding to the flux points, wherein the non-sticky flux at least comprises non-sticky flux in a conservation form and non-sticky flux in a non-conservation form; according to the non-sticky flux corresponding to the flux point, determining a first derivative of the non-sticky flux in a conservation form at the solving point and a first derivative of the non-sticky flux in a non-conservation form at the solving point; determining flux information at interfaces of grid cells, and determining correction information of non-sticky flux in a conservation form; determining discrete items of the non-sticky flux of the grid unit to be calculated according to the first derivative of the non-sticky flux in the conservation form at the solving point, the first derivative of the non-sticky flux in the non-conservation form at the solving point and the correction information of the non-sticky flux in the conservation form; according to the discrete items of the non-sticky flux of the grid unit to be calculated, the target non-sticky flux of the grid unit to be calculated is determined, and the embodiment of the invention constructs the derivative of the discontinuous flux polynomial by setting a group of flux points staggered with the solving points, and then applies a split form to the derivative, so that the constructed format can be ensured to meet the discrete conservation law, and the format is applied to a multi-scale structure, thereby improving the calculation stability.
Drawings
In order to more clearly illustrate the embodiments or prior art solutions of the present application, the drawings that are required for the description of the embodiments or prior art will be briefly described below, it being apparent that the drawings in the following description are only some of the embodiments described in the present application, and that other drawings may be obtained according to these drawings without inventive faculty for a person skilled in the art.
FIG. 1 is a flow chart of a calculation method of non-stick flux according to an embodiment of the present application;
FIG. 2 is a display diagram of a grid cell in accordance with one embodiment of the present application;
FIG. 3 is a display diagram of a grid cell according to yet another embodiment of the present application;
FIG. 4 is a block diagram of an embodiment of a non-stick flux computing device of the present application;
fig. 5 is a schematic structural diagram of a terminal device of the present application.
Detailed Description
For the purposes, technical solutions and advantages of the present application, the technical solutions of the present application will be clearly and completely described below with reference to specific embodiments and corresponding drawings. It will be apparent that the described embodiments are only some, but not all, of the embodiments of the present application. All other embodiments, which can be made by one of ordinary skill in the art without undue burden from the present disclosure, are within the scope of the present disclosure.
Noun interpretation:
NS equation: the abbreviation of the Navier-Stokes equation is used to describe the hydrodynamic control equation.
Euler equation: the NS equation is the equation obtained when the viscosity coefficient is taken to be 0.
Flow field variable: pressure, velocity, density, temperature, etc. in the flow.
CFD: computational Fluid Dynamics, the continuous NS equation is discretized by a numerical discrete method, so as to obtain the flow field variable distribution at a certain moment.
CPR method: correction Procedure via Reconstruction, for discrete NS equation, corrects the intermittent flux function by using the interface public flux to reconstruct the flux function, and further to calculate the flux derivative.
Split form: the convection term in the Euler equation is split into a combination of conservation terms and non-conservation terms.
LG point: the Legendre-Gauss point is a solution point type in CPR method.
An embodiment of the present application provides a method for calculating a non-stick flux of a grid cell. The execution body of the embodiment is a calculation device without adhesive flux, and is arranged on a terminal device, for example, the terminal device at least comprises a computer terminal and the like.
Referring to fig. 1, a flow chart of a method for calculating a non-stick flux according to an embodiment of the present application is shown, and the method may specifically include the following steps:
s101, acquiring a grid unit to be calculated, and determining solution points and flux points of the grid unit according to the grid unit;
as shown in fig. 2, fig. 2 shows a one-dimensional grid cell, on which the distribution solution points are Gauss-Legendre integral points, the number of flux points (squares) is one more than that of the solution points (circles) in each dimension, the distance between adjacent flux points is Gauss integral weight, and the flux points at two ends are distributed on the cell interface. If 3 is a grid unit in the two-dimensional case, the circular points in the figure are solution points, and the square points are flux points.
Wherein the grid may be a non-structural quadrilateral or hexahedral grid data structure.
S102, determining physical information corresponding to flux points according to preset initial conditions;
specifically, the terminal device can obtain the physical quantity at the solving point, namely the density, the pressure and the speed equivalent according to the initial condition (initial distribution of the flow field), and the physical quantity at the flux point can be obtained by constructing Lagrange interpolation polynomials at the solving point.
S103, calculating the non-sticky flux corresponding to the flux points according to the physical information corresponding to the flux points and the preset split form, wherein the non-sticky flux at least comprises the non-sticky flux in the conservation form and the non-sticky flux in the non-conservation form;
specifically, the terminal device calculates its corresponding non-stick flux, including the flux in the conservative form and the flux in the non-conservative form, according to the physical quantity at the flux point.
According to the split form, the non-stick flux is split into a combination of a partially conserved form and a partially non-conserved form, and the combination coefficients are different and correspond to different types of split forms.
S104, determining a first derivative of the non-sticky flux in a conservation form at a solving point and a first derivative of the non-sticky flux in a non-conservation form at the solving point according to the non-sticky flux corresponding to the flux point;
specifically, the usual split form types are Fe split, bl split, KG1 split, KG2 split, and the like, and the forms are as follows:
split form of Fe split Fe:
;
wherein,SPthe solution point is indicated as such,。
bl split form split Bl:
;
KG1 split form split KG1:
;
KG2 split form split KG2:
;
the calculation of each first derivative is obtained by deriving based on lagrange interpolation polynomials constructed by flux points and taking values at solving points.
S105, determining flux information at interfaces of the grid cells and determining correction information of non-sticky flux in a conservation mode;
specifically, the terminal equipment obtains correction terms of conservation type non-sticky flux derivatives, namely correction information, according to the numerical flux at the cell interface, such as Riemann flux and non-sticky flux at the cell interface, and by introducing left and right correction functions.
S106, determining a discrete item of the non-sticky flux of the grid unit to be calculated according to the first derivative of the non-sticky flux in the conservation form at the DCF solving point, the first derivative of the non-sticky flux in the non-conservation form at the DNCF solving point and the correction information DCF_corr of the non-sticky flux in the conservation form;
DF=DCF+DCF_corr+DNCF；
s107, determining the target non-stick flux of the grid unit to be calculated according to the discrete items of the non-stick flux of the grid unit to be calculated.
Specifically, for the convection term of the Euler equation, a split form is adopted to improve the calculation stability. In order to improve the calculation accuracy, LG points are used as solution points instead of LGL points. The present invention proposes constructing a split form CPR format in a staggered grid form to ensure conservation of the format. By configuring a group of flux points staggered with the solution points to construct the derivative of the discontinuous flux polynomial and then applying a split form to the derivative, the constructed format can be ensured to meet the discrete conservation law, and the format is applied to compressible turbulence simulation, so that the calculation stability is improved.
According to the calculation method of the non-sticky flux, the grid cells to be calculated are obtained, and flux points of the grid cells are determined according to the grid cells; determining physical information corresponding to flux points according to preset initial conditions; according to the physical information corresponding to the flux points and a preset split form, calculating the non-sticky flux corresponding to the flux points, wherein the non-sticky flux at least comprises non-sticky flux in a conservation form and non-sticky flux in a non-conservation form; according to the non-sticky flux corresponding to the flux point, determining a first derivative of the non-sticky flux in a conservation form at the solving point and a first derivative of the non-sticky flux in a non-conservation form at the solving point; determining flux information at interfaces of grid cells, and determining correction information of non-sticky flux in a conservation form; determining discrete items of the non-sticky flux of the grid unit to be calculated according to the first derivative of the non-sticky flux in the conservation form at the solving point, the first derivative of the non-sticky flux in the non-conservation form at the solving point and the correction information of the non-sticky flux in the conservation form; according to the discrete items of the non-sticky flux of the grid unit to be calculated, the target non-sticky flux of the grid unit to be calculated is determined, and the embodiment of the invention constructs the derivative of the discontinuous flux polynomial by setting a group of flux points staggered with the solving points, and then applies a split form to the derivative, so that the constructed format can be ensured to meet the discrete conservation law, and the format is applied to a multi-scale structure, thereby improving the calculation stability.
In another embodiment of the present application, the method for calculating the non-stick flux provided in the above embodiment is further described in a supplementary manner.
Optionally, calculating the non-sticky flux corresponding to the flux point according to the physical information corresponding to the flux point and the preset split form, including:
according to a preset splitting form, splitting the non-stick flux corresponding to the flux point into a combination of the non-stick flux in a conservation form and the non-stick flux in a non-conservation form, wherein the non-stick flux in the combination is split into a combination coefficient of the non-stick flux in the conservation form and the non-stick flux in the non-conservation form, and the combination coefficient is different.
Alternatively, the solution points are gaussian points and the solution points and flux points are staggered.
Optionally, determining physical information corresponding to the flux point according to a preset initial condition includes:
calculating physical information corresponding to the solving points according to preset initial conditions, wherein the preset initial conditions at least comprise flow field initial conditions, and the physical information at least comprises one or more of density, pressure and speed;
and constructing a Lagrange interpolation polynomial at the solving point to obtain physical information corresponding to the flux point.
Optionally, determining the first derivative of the non-stick flux in the conservation form at the solution point and the first derivative of the non-stick flux in the non-conservation form at the solution point according to the non-stick flux corresponding to the flux point includes:
Determining a first derivative of the non-stick flux in the conservation form at the solution point according to the non-stick flux in the conservation form at the flux point;
from the non-stick flux in the non-conservative form at the flux point, a first derivative of the non-stick flux in the non-conservative form at the solution point is determined.
Optionally, determining flux information at the interface of the grid cells, determining correction information for non-stick flux in a conservation form, comprising:
calculating Riemann flux at interfaces of the grid cells and non-stick flux at the interfaces;
and obtaining correction information of the non-sticky flux in a conservation form according to the left and right correction functions of the flux points at the interfaces.
The invention provides a split-form-based non-sticky flux calculation method, which is used for removing confusion errors and realizing stable non-sticky flux calculation of an NS equation.
The specific steps of the stabilized non-tacky flux calculation based on the split form of the NS equation include:
step 1: on the grid unit, the distribution solving points are Legendre-Gauss integrating points, and the number of flux points is one more than that of the solving points according to each dimension. The distance between adjacent flux points is Gauss integral weight, the flux points at two ends are distributed on a unit interface, and the flux points are staggered with the solving points. In the one-dimensional case, when the number of solution points is 5, the arrangement mode is shown in fig. 2.
Wherein the circles represent solution points and the boxes represent flux points. In the two-dimensional case, the arrangement of the solution points and the flux points is shown in fig. 3.
Step 2: according to the split form, the non-stick flux is split into a combination of a partially conserved form and a partially non-conserved form, and the combination coefficients are different and correspond to different types of split forms.
Step 3: according to the initial conditions (initial distribution of the flow field), the physical quantity at the solving point, namely the density, the pressure and the speed equivalent, can be obtained, and the physical quantity at the flux point can be obtained by constructing Lagrange interpolation polynomials at the solving point.
Step 4: based on the physical quantity at the flux point, the corresponding non-stick flux is calculated, including the flux in the conservative form and the flux in the non-conservative form.
Step 5: from the non-stick flux at the flux point, a first derivative of the conservation form non-stick flux at the solution point and a first derivative of the non-conservation form non-stick flux at the solution point are calculated, the two first derivative terms being part of the conservation form non-stick flux derivative.
Step 6: and according to the Riemann flux at the cell interface and the non-viscous flux at the cell interface, introducing left and right correction functions to obtain a correction term of the conservation-form non-viscous flux derivative.
Step 7: and (3) obtaining discrete items based on the conservation form non-viscous flux derivative of the split form according to the two first derivative items obtained in the step (5) and the correction item obtained in the step (6).
The calculation method for guaranteeing conservation of split CPR format based on LG points for non-sticky flux, disclosed by the embodiment of the invention, has the following technical effects: the use of LG points as solution points for the split form CPR format has a higher accuracy than LGL points. On the premise of not influencing the calculation stability, four typical split form CPR formats based on LG points can be ensured to all meet the discrete conservation law, and the applicability is stronger.
It should be noted that, for simplicity of description, the method embodiments are shown as a series of acts, but it should be understood by those skilled in the art that the embodiments are not limited by the order of acts described, as some steps may occur in other orders or concurrently in accordance with the embodiments. Further, those skilled in the art will appreciate that the embodiments described in the specification are all preferred embodiments and that the acts referred to are not necessarily required by the embodiments of the present application.
According to the calculation method of the non-sticky flux, the grid cells to be calculated are obtained, and flux points of the grid cells are determined according to the grid cells; determining physical information corresponding to flux points according to preset initial conditions; according to the physical information corresponding to the flux points and a preset split form, calculating the non-sticky flux corresponding to the flux points, wherein the non-sticky flux at least comprises non-sticky flux in a conservation form and non-sticky flux in a non-conservation form; according to the non-sticky flux corresponding to the flux point, determining a first derivative of the non-sticky flux in a conservation form at the solving point and a first derivative of the non-sticky flux in a non-conservation form at the solving point; determining flux information at interfaces of grid cells, and determining correction information of non-sticky flux in a conservation form; determining discrete items of the non-sticky flux of the grid unit to be calculated according to the first derivative of the non-sticky flux in the conservation form at the solving point, the first derivative of the non-sticky flux in the non-conservation form at the solving point and the correction information of the non-sticky flux in the conservation form; according to the discrete items of the non-sticky flux of the grid unit to be calculated, the target non-sticky flux of the grid unit to be calculated is determined, and the embodiment of the invention constructs the derivative of the discontinuous flux polynomial by setting a group of flux points staggered with the solving points, and then applies a split form to the derivative, so that the constructed format can be ensured to meet the discrete conservation law, and the format is applied to a multi-scale structure, thereby improving the calculation stability.
Another embodiment of the present application provides a non-stick flux calculating device, configured to perform the non-stick flux calculating method provided in the foregoing embodiment.
Referring to fig. 4, there is shown a block diagram of an embodiment of a non-stick flux computing device of the present application, which may include the following modules in particular: an acquisition module 401, a first determination module 402, a second determination module 403, a third determination module 404, a fourth determination module 405, a correction module 406, and a fifth determination module 407, wherein:
the acquisition module 401 is configured to acquire a grid cell to be calculated, and determine flux points of the grid cell according to the grid cell;
the first determining module 402 is configured to determine physical information corresponding to the flux point according to a preset initial condition;
the second determining module 403 is configured to calculate, according to the physical information corresponding to the flux point and the preset split form, an unbounded flux corresponding to the flux point, where the unbounded flux at least includes an unbounded flux in a conservative form and an unbounded flux in a non-conservative form;
the third determining module 404 is configured to determine, according to the non-sticky flux corresponding to the flux point, a first derivative of the non-sticky flux in a conservation form at the solution point and a first derivative of the non-sticky flux in a non-conservation form at the solution point;
The fourth determining module 405 is configured to determine flux information at interfaces of the grid cells, and determine correction information of the non-stick flux in the conservation form;
the correction module 406 is configured to determine a discrete term of the non-sticky flux of the grid unit to be calculated according to the first derivative of the non-sticky flux in the conservation form at the solution point, the first derivative of the non-sticky flux in the non-conservation form at the solution point, and the correction information of the non-sticky flux in the conservation form;
the fifth determining module 407 is configured to determine the target non-stick flux of the grid cell to be calculated according to the discrete term of the non-stick flux of the grid cell to be calculated.
According to the non-sticky flux calculating device, the grid cells to be calculated are obtained, and flux points of the grid cells are determined according to the grid cells; determining physical information corresponding to flux points according to preset initial conditions; according to the physical information corresponding to the flux points and a preset split form, calculating the non-sticky flux corresponding to the flux points, wherein the non-sticky flux at least comprises non-sticky flux in a conservation form and non-sticky flux in a non-conservation form; according to the non-sticky flux corresponding to the flux point, determining a first derivative of the non-sticky flux in a conservation form at the solving point and a first derivative of the non-sticky flux in a non-conservation form at the solving point; determining flux information at interfaces of grid cells, and determining correction information of non-sticky flux in a conservation form; determining discrete items of the non-sticky flux of the grid unit to be calculated according to the first derivative of the non-sticky flux in the conservation form at the solving point, the first derivative of the non-sticky flux in the non-conservation form at the solving point and the correction information of the non-sticky flux in the conservation form; according to the discrete items of the non-sticky flux of the grid unit to be calculated, the target non-sticky flux of the grid unit to be calculated is determined, and the embodiment of the invention constructs the derivative of the discontinuous flux polynomial by setting a group of flux points staggered with the solving points, and then applies a split form to the derivative, so that the constructed format can be ensured to meet the discrete conservation law, and the format is applied to a multi-scale structure, thereby improving the calculation stability.
A further embodiment of the present application further provides a non-stick flux computing device provided by the above embodiment.
Optionally, the second determining module is configured to:
according to a preset splitting form, splitting the non-stick flux corresponding to the flux point into a combination of the non-stick flux in a conservation form and the non-stick flux in a non-conservation form, wherein the non-stick flux in the combination is split into a combination coefficient of the non-stick flux in the conservation form and the non-stick flux in the non-conservation form, and the combination coefficient is different.
Alternatively, the solution points are gaussian points and the solution points and flux points are staggered.
Optionally, the first determining module is configured to:
calculating physical information corresponding to the solving points according to preset initial conditions, wherein the preset initial conditions at least comprise flow field initial conditions, and the physical information at least comprises one or more of density, pressure and speed;
and constructing a Lagrange interpolation polynomial at the solving point to obtain physical information corresponding to the flux point.
Optionally, the third determining module is configured to:
determining a first derivative of the non-stick flux in the conservation form at the solution point according to the non-stick flux in the conservation form at the flux point;
from the non-stick flux in the non-conservative form at the flux point, a first derivative of the non-stick flux in the non-conservative form at the solution point is determined.
Optionally, the correction module is configured to:
calculating a Riemann flux at the interface of the grid cells and a non-stick flux at the interface;
and obtaining correction information of the non-sticky flux in a conservation form according to the left and right correction functions of the flux points at the interfaces.
For the device embodiments, since they are substantially similar to the method embodiments, the description is relatively simple, and reference is made to the description of the method embodiments for relevant points.
According to the non-sticky flux calculating device, the grid cells to be calculated are obtained, and flux points of the grid cells are determined according to the grid cells; determining physical information corresponding to flux points according to preset initial conditions; according to the physical information corresponding to the flux points and a preset split form, calculating the non-sticky flux corresponding to the flux points, wherein the non-sticky flux at least comprises non-sticky flux in a conservation form and non-sticky flux in a non-conservation form; according to the non-sticky flux corresponding to the flux point, determining a first derivative of the non-sticky flux in a conservation form at the solving point and a first derivative of the non-sticky flux in a non-conservation form at the solving point; determining flux information at interfaces of grid cells, and determining correction information of non-sticky flux in a conservation form; determining discrete items of the non-sticky flux of the grid unit to be calculated according to the first derivative of the non-sticky flux in the conservation form at the solving point, the first derivative of the non-sticky flux in the non-conservation form at the solving point and the correction information of the non-sticky flux in the conservation form; according to the discrete items of the non-sticky flux of the grid unit to be calculated, the target non-sticky flux of the grid unit to be calculated is determined, and the embodiment of the invention constructs the derivative of the discontinuous flux polynomial by setting a group of flux points staggered with the solving points, and then applies a split form to the derivative, so that the constructed format can be ensured to meet the discrete conservation law, and the format is applied to a multi-scale structure, thereby improving the calculation stability.
An embodiment of the present application provides a terminal device, configured to execute the method for calculating the non-sticky flux provided in the embodiment.
Fig. 5 is a schematic structural diagram of a terminal device of the present application, as shown in fig. 5, including: at least one processor 501 and memory 502;
the memory stores a computer program; the at least one processor executes the computer program stored in the memory to implement the non-stick flux calculation method provided by the above embodiment.
The terminal equipment provided by the embodiment determines flux points of the grid cells by acquiring the grid cells to be calculated and according to the grid cells; determining physical information corresponding to flux points according to preset initial conditions; according to the physical information corresponding to the flux points and a preset split form, calculating the non-sticky flux corresponding to the flux points, wherein the non-sticky flux at least comprises non-sticky flux in a conservation form and non-sticky flux in a non-conservation form; according to the non-sticky flux corresponding to the flux point, determining a first derivative of the non-sticky flux in a conservation form at the solving point and a first derivative of the non-sticky flux in a non-conservation form at the solving point; determining flux information at interfaces of grid cells, and determining correction information of non-sticky flux in a conservation form; determining discrete items of the non-sticky flux of the grid unit to be calculated according to the first derivative of the non-sticky flux in the conservation form at the solving point, the first derivative of the non-sticky flux in the non-conservation form at the solving point and the correction information of the non-sticky flux in the conservation form; according to the discrete items of the non-sticky flux of the grid unit to be calculated, the target non-sticky flux of the grid unit to be calculated is determined, and the embodiment of the invention constructs the derivative of the discontinuous flux polynomial by setting a group of flux points staggered with the solving points, and then applies a split form to the derivative, so that the constructed format can be ensured to meet the discrete conservation law, and the format is applied to a multi-scale structure, thereby improving the calculation stability.
Yet another embodiment of the present application provides a computer readable storage medium having a computer program stored therein, which when executed implements the method for calculating a non-stick flux provided in any one of the above embodiments.
According to the computer-readable storage medium of the present embodiment, flux points of grid cells are determined by acquiring the grid cells to be calculated and according to the grid cells; determining physical information corresponding to flux points according to preset initial conditions; according to the physical information corresponding to the flux points and a preset split form, calculating the non-sticky flux corresponding to the flux points, wherein the non-sticky flux at least comprises non-sticky flux in a conservation form and non-sticky flux in a non-conservation form; according to the non-sticky flux corresponding to the flux point, determining a first derivative of the non-sticky flux in a conservation form at the solving point and a first derivative of the non-sticky flux in a non-conservation form at the solving point; determining flux information at interfaces of grid cells, and determining correction information of non-sticky flux in a conservation form; determining discrete items of the non-sticky flux of the grid unit to be calculated according to the first derivative of the non-sticky flux in the conservation form at the solving point, the first derivative of the non-sticky flux in the non-conservation form at the solving point and the correction information of the non-sticky flux in the conservation form; according to the discrete items of the non-sticky flux of the grid unit to be calculated, the target non-sticky flux of the grid unit to be calculated is determined, and the embodiment of the invention constructs the derivative of the discontinuous flux polynomial by setting a group of flux points staggered with the solving points, and then applies a split form to the derivative, so that the constructed format can be ensured to meet the discrete conservation law, and the format is applied to a multi-scale structure, thereby improving the calculation stability.
It should be noted that the foregoing detailed description is exemplary and is intended to provide further explanation of the invention. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments in accordance with the present application. As used herein, the singular is intended to include the plural unless the context clearly indicates otherwise. Furthermore, it will be further understood that the terms "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, steps, operations, devices, components, and/or groups thereof.
It should be noted that the terms "first," "second," and the like in the description and claims of the present application and the above figures are used for distinguishing between similar objects and not necessarily for describing a particular sequential or chronological order. It is to be understood that the terms so used are interchangeable under appropriate circumstances such that the embodiments of the application described herein are capable of operation in sequences other than those illustrated or otherwise described herein.
Furthermore, the terms "comprise" and "have," as well as any variations thereof, are intended to cover a non-exclusive inclusion. For example, a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those elements but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
Spatially relative terms, such as "above … …," "above … …," "upper surface at … …," "above," and the like, may be used herein for ease of description to describe one device or feature's spatial location relative to another device or feature as illustrated in the figures. It will be understood that the spatially relative terms are intended to encompass different orientations in use or operation in addition to the orientation depicted in the figures. For example, if the device in the figures is turned over, elements described as "above" or "over" other devices or structures would then be oriented "below" or "beneath" the other devices or structures. Thus, the exemplary term "above … …" may include both orientations of "above … …" and "below … …". The device may also be positioned in other different ways, such as rotated 90 degrees or at other orientations, and the spatially relative descriptors used herein interpreted accordingly.
In the above detailed description, reference is made to the accompanying drawings, which form a part hereof. In the drawings, like numerals typically identify like components unless context indicates otherwise. The illustrated embodiments described in the detailed description, drawings, and claims are not meant to be limiting. Other embodiments may be utilized, and other changes may be made, without departing from the spirit or scope of the subject matter presented herein.
The foregoing is merely a preferred embodiment of the present application and is not intended to limit the present application, and various modifications and variations may be made to the present application by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application should be included in the protection scope of the present application.
Claims (8)
1. A method of calculation of a non-stick flux, the method comprising:
acquiring a grid unit to be calculated, and determining solving points and flux points of the grid unit according to the grid unit;
determining physical information corresponding to flux points according to preset initial conditions;
calculating the non-sticky flux corresponding to the flux point according to the physical information corresponding to the flux point and a preset split form, wherein the non-sticky flux at least comprises the non-sticky flux in a conservation form and the non-sticky flux in a non-conservation form;
According to the non-sticky flux corresponding to the flux point, determining a first derivative of the non-sticky flux in a conservation form at the flux point and a first derivative of the non-sticky flux in a non-conservation form at the flux point;
determining flux information at interfaces of the grid cells, and determining correction information of non-sticky flux in a conservation form;
determining a discrete item of the non-sticky flux of the grid unit to be calculated according to the first derivative of the non-sticky flux in the conservation form at the flux point, the first derivative of the non-sticky flux in the non-conservation form at the flux point and the correction information of the non-sticky flux in the conservation form;
determining the target non-stick flux of the grid unit to be calculated according to the discrete items of the non-stick flux of the grid unit to be calculated;
the method for obtaining the grid unit to be calculated and determining the solving point and the flux point of the grid unit according to the grid unit comprises the following steps:
on the grid unit, distributing solving points are Gauss-Legendre integrating points, the number of flux points is one more than that of the solving points according to each dimension, the distance between adjacent flux points is Gauss integrating weight, and the flux points at two ends are distributed on a grid interface;
According to the physical information corresponding to the flux points and a preset split form, calculating the non-stick flux corresponding to the flux points, wherein the non-stick flux at least comprises the non-stick flux in a conservation form and the non-stick flux in a non-conservation form, and the non-stick flux comprises the following components:
splitting the non-stick flux corresponding to the flux point into a combination of the non-stick flux in a conservation form and the non-stick flux in a non-conservation form according to a preset splitting form, wherein the non-stick flux in the combination is split into a combination coefficient of the non-stick flux in the conservation form and the non-stick flux in the non-conservation form to be different;
the determining flux information at the interfaces of the grid cells, determining correction information for non-stick flux in a conservation form, comprising:
and according to the numerical flux at the cell interface, introducing left and right correction functions to obtain correction information of the conservation-form non-viscous flux derivative.
2. The method of claim 1, wherein the solution points are gaussian points and the solution points and the flux points are staggered.
3. The method of claim 1, wherein determining physical information corresponding to the flux points according to the preset initial conditions comprises:
Calculating physical information corresponding to the solving point according to the preset initial conditions, wherein the preset initial conditions at least comprise flow field initial conditions, and the physical information at least comprises one or more of density, pressure and speed;
and constructing a Lagrange interpolation polynomial at the solving point to obtain physical information corresponding to the flux point.
4. The method of claim 1, wherein determining the first derivative of the non-stick flux in the conservative form at the flux point and the first derivative of the non-stick flux in the non-conservative form at the flux point based on the non-stick flux corresponding to the flux point comprises:
determining a first derivative of the non-stick flux in the conservation form at the flux point from the non-stick flux in the conservation form at the flux point;
determining a first derivative of the non-stick flux in the non-conservative form at the flux point from the non-stick flux in the non-conservative form at the flux point.
5. The method of claim 1, wherein the determining flux information at the interface of the grid cells, determining correction information for non-stick flux in a conservative form, comprises:
Calculating the Riemann flux at the interface of the grid cells and the non-sticking flux at the interface;
and obtaining correction information of the non-sticky flux in a conservation form according to the left and right correction functions of the flux points at the interfaces.
6. A non-stick flux computing device, the device comprising:
the acquisition module is used for acquiring the grid cells to be calculated and determining flux points of the grid cells according to the grid cells;
the first determining module is used for determining physical information corresponding to the flux points according to preset initial conditions;
the second determining module is used for calculating the non-sticky flux corresponding to the flux point according to the physical information corresponding to the flux point and a preset split form, wherein the non-sticky flux at least comprises the non-sticky flux in a conservation form and the non-sticky flux in a non-conservation form;
the third determining module is used for determining a first derivative of the non-stick flux in a conservation form at the flux point and a first derivative of the non-stick flux in a non-conservation form at the flux point according to the non-stick flux corresponding to the flux point;
a fourth determining module, configured to determine flux information at interfaces of the grid cells, and determine correction information of non-sticky flux in a conservation form;
A correction module, configured to determine a discrete term of the non-sticky flux of the grid unit to be calculated according to a first derivative of the non-sticky flux in a conservation form at the flux point, a first derivative of the non-sticky flux in a non-conservation form at the flux point, and correction information of the non-sticky flux in the conservation form;
a fifth determining module, configured to determine a target non-sticky flux of the grid unit to be calculated according to discrete terms of the non-sticky flux of the grid unit to be calculated;
wherein, the acquisition module is used for:
on the grid unit, distributing solving points are Gauss-Legendre integrating points, the number of flux points is one more than that of the solving points according to each dimension, the distance between adjacent flux points is Gauss integrating weight, and the flux points at two ends are distributed on a grid interface;
the second determining module is configured to:
splitting the non-stick flux corresponding to the flux point into a combination of the non-stick flux in a conservation form and the non-stick flux in a non-conservation form according to a preset splitting form, wherein the non-stick flux in the combination is split into a combination coefficient of the non-stick flux in the conservation form and the non-stick flux in the non-conservation form to be different;
The fourth determining module is configured to:
and according to the numerical flux at the cell interface, introducing left and right correction functions to obtain correction information of the conservation-form non-viscous flux derivative.
7. A terminal device, comprising: at least one processor and memory;
the memory stores a computer program; the at least one processor executes the computer program stored by the memory to implement the non-stick flux calculation method of any one of claims 1-5.
8. A computer readable storage medium, characterized in that a computer program is stored in the computer readable storage medium, which computer program, when executed, implements the non-stick flux calculation method according to any one of claims 1-5.
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