CN112733403B - Method for limiting viscous item in flow equation - Google Patents
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- CN112733403B CN112733403B CN202011622593.7A CN202011622593A CN112733403B CN 112733403 B CN112733403 B CN 112733403B CN 202011622593 A CN202011622593 A CN 202011622593A CN 112733403 B CN112733403 B CN 112733403B
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Abstract
The invention discloses a method for limiting a viscosity term in a flow equation, which optimizes a formula for calculating a quantity value of the viscosity term and limits the minimum value of an included angle a of adjacent grids obtained by calculation for grids with quality not meeting the calculation requirement, thereby reducing the divergence in the calculation process. The invention provides a method for limiting a viscosity term in a flow equation, wherein in the solving process of the flow equation, in order to avoid irrationality of calculation of the viscosity term caused by grid distortion, a limiter for calculation of the viscosity term is designed, and calculation divergence of CFD (computational fluid dynamics) calculation software in poor grid quality is avoided, so that the robustness of the CFD calculation software is ensured.
Description
Technical Field
The present invention relates to the field of hydrodynamics. More particularly, the present invention relates to a system for limiting the viscous term in a flow equation in Computational Fluid Dynamics (CFD).
Background
Computational Fluid Dynamics (CFD) refers to the use of numerical methods and formats to solve governing equations of fluid motion in a discrete grid system, such as the Navier-Stokes equation for viscous flow. The generation quality of the discrete grid system depends on the complexity of the appearance, for the appearance with a very complex topological structure, the orthogonality of the generated grid is often poor, the grid quality is not high, at the moment, the precision of a calculation result is influenced, and unstable calculation and divergence of a calculation process can be caused. Numerical calculation experience and analysis show that the main reason for divergence of the calculation process is that the calculation of the viscosity term is unreasonable, the smaller the grid included angle is, the larger the calculation of the viscosity term is, and non-physical viscosity quantity exists.
In the CFD numerical solution process, the grid quality has great influence on the calculation result. In addition to reducing the format accuracy of numerical solution, sometimes the grid quality is too poor, so that the calculation process is diverged and the calculation software crashes. However, the grid quality is sometimes difficult to guarantee, especially for the flow field with a complicated shape, and it is difficult for an inexperienced user to generate a high-quality grid. Therefore, if the robustness problem of the computing software can be solved by a numerical processing method, the difficulty of generating the grid can be greatly reduced, and the over-high requirement on quality in the grid generating process is avoided.
The graph shown in FIG. 4 illustrates one aspect of grid quality, with DA less than 45 degrees and DB close to 90 degrees, so that grid quality at DB is better than DA. When the angle is too small (called grid distortion), the accuracy of computing the sticky term is poor, an unreasonably large magnitude is obtained, and the magnitude is non-physical, so that the stability of the computing method is lost, and finally the divergence of the computing process is caused, namely the crash of computing software is caused.
In the prior art, once an unreasonable physical quantity appears in a calculation process, the physical quantity needs to be limited to be in a reasonable interval. In the prior art, only the physical quantity of the flow field is limited by a threshold value. The restriction is not clear about the mechanism of generating the non-physical quantity in the calculation process, only the final result is limited, and the inherent factors of generating the non-physical quantity cannot be eliminated, so that the restriction process always exists, and the quality of the final result is not high.
Disclosure of Invention
An object of the present invention is to solve at least the above problems and/or disadvantages and to provide at least the advantages described hereinafter.
To achieve these objects and other advantages and in accordance with the purpose of the invention, as embodied and broadly described herein, a method for constraining a viscous term in a flow equation is provided, wherein a formula for calculating a magnitude of the viscous term is optimized for a mesh whose quality does not satisfy a calculation requirement, and a minimum value of an included angle a between adjacent meshes obtained by calculation is constrained, thereby reducing a divergence in the calculation process.
Preferably, the calculation formula of the calculation amount of the viscosity term is configured to adopt:
T xy ＝(U 2 -U 1 )/d；
wherein, the (U) 2 -U 1 ) Is the difference in horizontal velocity between the center points of adjacent grids, and d is the normal distance between the center points of adjacent grids.
Preferably, the defining method is configured to include:
limiting the included angle a of adjacent grids, and controlling the range of the included angle a to be [0, pi ];
when a > pi/2, a = pi-a;
setting the minimum limit range of a to be epsilon, and if a < epsilon, alim = epsilon; otherwise, alim = a.
The value of d is calculated using the formula d = L sin (alim), where L is the straight-line distance between 1 and 2 points.
Preferably, the limit range of the minimum value epsilon of the included angles between the adjacent grids is controlled to be 0.1-0.2.
The invention at least comprises the following beneficial effects: in the process of solving the flow equation, in order to avoid irrationality of calculation of the viscous term caused by grid distortion, the invention designs the limiter aiming at calculation of the viscous term, and avoids calculation divergence of CFD calculation software when the grid quality is poor, thereby ensuring the robustness of the CFD calculation software.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention.
Drawings
FIG. 1 is a grid diagram of a derived viscosity term calculation magnitude formula in accordance with the present invention;
FIG. 2 is a schematic diagram of a grid with triangles as calculation regions;
FIG. 3 is a schematic diagram of a grid with circles as calculation regions;
fig. 4 is a diagram illustrating grid quality comparison.
Detailed Description
The present invention is described in further detail below to enable those skilled in the art to practice the invention with reference to the description.
The inherent mechanism that the grid distortion causes the non-physical phenomenon to appear is mainly derived from that the viscous term is calculated to cause the excessively large value of the viscous term, and the balance between the convection term and the viscous term in the equation is disturbed. This excessive sticky term magnitude is not practical and is a result of both the computational method and the distortion mesh.
For the grids with the quality which does not meet the calculation requirement, the formula of the calculated value of the viscosity term is optimized, and the minimum value of the included angle a between the adjacent grids obtained by calculation is limited, so that the divergence of the calculation process is reduced.
Specifically, the calculation formula of the calculation amount of the viscosity term is configured to employ:
T xy ＝(U 2 -U 1 )/d；
wherein, the (U) 2 -U 1 ) Is the difference in horizontal velocity between the center points of adjacent grids, and d is the normal distance between the center points of adjacent grids.
According to the stress formula and with reference to fig. 1, it can be seen that 1 and 2 are respectively the central points of two adjacent grids, the vertical distance between two points is d, the included angle between the two points is a, u is the horizontal velocity between the two points, and then the tangential stress on the grid boundary between the two points is the velocity difference between the two points divided by the vertical distance (normal distance) d, so that the calculation scheme of the tangential stress is provided, that is, the central point difference value is divided by the normal distance between the two points to replace the conventional gaussian theorem, so as to ensure the later calculation effect, and the substantial calculation process is as described above no matter how the mathematical formula form changes.
When the grid distortion is large, i.e. a deviates much from 90 degrees, close to 0 degrees or 180 degrees, then d is close to 0, at which time the calculated tangential stress is abnormally large and must be limited. The following limiting method is for angle a (in radians below):
(1) The range of a: [0, π ]
(2) If a > π/2, a = π -a;
(3) Setting a minimum limit range epsilon of a, and if a < epsilon, alim = epsilon; otherwise, alim = a.
(4) The d value, d = L sin (alim), is calculated, where L is the straight-line distance between 1 and 2 points.
The choice of e is usually related to the experience of whether a software crash occurs, and in order to avoid loss of accuracy as much as possible, 0.1 radians, which corresponds to about 5 degrees, can be chosen. In the scheme, a limiting mode is provided, namely the minimum value of the grid included angle obtained through calculation is limited, the limiting range is about 0.1-0.2 radian, and software practice proves that the limitation of the calculation of the viscosity item is effective, so that the robustness of software is improved.
In the process of CFD calculating the related problem of complex shape, the grid generation is a very critical link, if the numerical method does not carry out special treatment, the requirement on the grid generation is very high, and the workload of the grid generation is greatly increased. Especially for structural grid systems. The following is a triangular or circular calculation area, if a structural mesh is to be generated, one or more edges of the structural mesh need to be truncated to form a quadrilateral, which inevitably results in a mesh angle of 180 degrees in one or more meshes of the structural mesh.
As shown in fig. 2-3. Because the included angle between the two grid edges is 180 degrees, the distance from the central point of the grid to the edge length is close to 0, the obtained tangential stress is close to infinity, and the calculation divergence is caused. Therefore, in general commercial software, such grids are defined as bad grid points, grid check cannot pass, and calculation cannot be carried out.
However, the grid generation mode can flexibly process various shapes and convert the shapes into structural grids, the grid generation process is greatly simplified, and if a computing program can process the grids, the adaptability of computing software can be greatly improved. If the sticky term limiter proposed by the present invention is used, it will not cause calculation divergence. The calculation software can obtain a more reasonable result for the grid with poor quality, and the robustness of the calculation software is good.
When the scheme of the invention is applied to different grids for calculation, compared with the prior art, the scheme ensures that the later calculation divergence is small by limiting the viscosity item, and the robustness of the software can be effectively improved.
In practical application, the method is applied to wind tunnel experiments for calculating hydrodynamics in aerospace engineering, for example, in the process of solving the thermal environment of a hypersonic aircraft, for grids with the quality not meeting the calculation requirement, the viscous item dispersion in the formula can be limited, the calculation divergence is controlled, and the excellence of the result is ensured by optimizing the formula for calculating the quantity value of the viscous item.
The method can be obtained according to a calculation result similar to the appearance of the space shuttle and comparison of calculation and experimental data, the robustness of software (the system maintains the characteristics of other certain performances under the condition of parameter perturbation of a certain structure and size) is effectively improved, and the calculation and experimental data are in good accordance, so that the method can well solve the practical engineering problem and partially replace the wind tunnel experimental result.
The above scheme is merely illustrative of a preferred example, and is not limiting. When the invention is implemented, appropriate replacement and/or modification can be carried out according to the requirements of users.
The number of apparatuses and the scale of the process described herein are intended to simplify the description of the present invention. Applications, modifications and variations of the present invention will be apparent to those skilled in the art.
While embodiments of the invention have been disclosed above, it is not intended to be limited to the uses set forth in the specification and examples. It can be applied to all kinds of fields suitable for the present invention. Additional modifications will readily occur to those skilled in the art. It is therefore intended that the invention not be limited to the exact details and illustrations described and illustrated herein, but fall within the scope of the appended claims and equivalents thereof.
Claims (2)
1. A method for limiting a viscosity term in a flow equation is characterized in that for grids with quality which does not meet the calculation requirements, the formula for calculating the quantity value of the viscosity term is optimized, and the minimum value of the included angle a between adjacent grids obtained through calculation is limited, so that the divergence of the calculation process is reduced;
the calculation formula of the calculation magnitude of the viscosity term is configured to employ:
T xy ＝(U 2 -U 1 )/d；
wherein, the (U) 2 -U 1 ) Is the difference in horizontal velocity between the center points of adjacent grids, and d is the normal distance between the center points of adjacent grids；
The limiting method is configured to include:
limiting the included angle a of adjacent grids, and controlling the range of the included angle a to be [0, pi ];
when a > pi/2, a = pi-a;
setting the minimum limiting range of a to be epsilon, and if a < epsilon, alim = epsilon; otherwise, alim = a;
the value of d is calculated using the formula d = L sin (alim), where L is the straight-line distance between 1 and 2 points.
2. The method for limiting the viscous term in a flow equation of claim 1, wherein the limit of the minimum value e of the adjacent grid angles is controlled within a range of 0.1 to 0.2 radians.
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| CN104636566A (en) * | 2015-03-13 | 2015-05-20 | 中国矿业大学 | Dynamic mesh numerical solution method based on modified fluid motion equation |
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