Strong shear turbulence grid adaptive simulation method coupled with SA series model

Abstract

The invention discloses a strong shear turbulence grid adaptive simulation method coupled with an SA series model. The method mainly comprises the following steps of: 1, judging whether a shielding function is applied or not; step 2, identifying a self-adaptive length scale of a shear layer; 3, constructing a scale-related adjustment function based on the turbulence energy spectrum integral; 4, reconstructing the turbulence viscosity of the SA series model by using an adjustment function; and 5, performing turbulence simulation by using the reconstructed turbulence viscosity. According to the method, the self-adaptive sub-grid length scale of the shear layer is constructed and introduced into the initial region of the quasi-two-dimensional free shear layer, so that the sub-grid length scale of the initial region of the free shear layer is effectively reduced, and the problem that an existing RANS-LES hybrid model is highly dependent on grids is solved. The calculation accuracy is improved, meanwhile, the calculation consumption is greatly reduced, the turbulence simulation process is remarkably accelerated, and an effective numerical simulation method is provided for solving low-consumption and high-precision simulation of strong shear flow in the complex engineering flow problem.

Description

Technical Field

[0001] The present invention relates to the field of complex fluid mechanics calculations for aeroengines and gas turbines, and in particular to a strongly sheared turbulent grid adaptive simulation method that couples SA series models. Background Art

[0002] Turbulence phenomena widely exist in nature and engineering fields. Among them, strongly sheared flows are complex turbulent types that cannot be ignored in many engineering applications. Strongly sheared flows are usually accompanied by extremely large velocity gradients and the interaction between large-scale and small-scale turbulences, and have flow characteristics such as non-equilibrium transport and anisotropy. Achieving accurate prediction of strongly sheared turbulence is a major challenge in current turbulence research. In order to improve the accuracy and reliability of engineering design, there is an urgent need to develop a turbulence simulation method that can accurately capture the characteristics of strongly sheared flows, is efficient and scalable.

[0003] The commonly used turbulence simulation methods in existing engineering mainly solve the Reynolds-averaged N-S (RANS) equations. Although the computational cost is small, the prediction accuracy for multi-scale, unsteady flows and complex flows with non-equilibrium transport and anisotropic turbulence is not good, and it is difficult to achieve refined research on complex flow mechanisms, which severely restricts the improvement of the design level in fields such as fluid machinery. As a high-precision numerical simulation method, the large eddy simulation (LES) method has high accuracy, but its computational cost is much higher than the level that can be tolerated in engineering applications. Under the existing computing power, it is difficult for the LES method to be applied to the flow prediction in complex engineering fields at the engineering design level.

[0004] In the past two decades, the RANS-LES hybrid simulation method has balanced the computational accuracy and computational efficiency by using the RANS method in the near-wall region and the LES method in the mainstream region, providing a good solution to the problem of high computational cost for high-precision simulation of complex flows. However, the classical RANS-LES hybrid model has relatively strict requirements for grids and requires users to have rich experience in high-precision numerical simulation, so its prediction ability for complex engineering flows is limited. Currently, various new types of grid adaptive turbulence simulations have been proposed, which can effectively improve the prediction ability for complex flows, but the definition of their grid scales cannot adapt to complex geometric grids, and a more suitable grid length scale needs to be combined for strongly sheared layers.

[0005] In order to improve the accuracy of the RANS-LES hybrid simulation of strong-shear turbulence, the present invention proposes a shear-layer adaptive subgrid length scale. By introducing this scale in the initial region of the quasi-two-dimensional free shear layer, the subgrid length scale in the initial region of the free shear layer is effectively reduced, and the accuracy and efficiency of the turbulence simulation in the shear layer are improved without significantly increasing the computational cost, thus providing a new approach to solve complex turbulent flow problems. Compared with the publicly disclosed invention patents CN117763838A and CN 117763995A, the influence of strongly anisotropic grids on the development of the shear layer can be significantly reduced, the prediction accuracy of the grid-adaptive turbulence simulation method can be further improved, and the computational cost can be effectively reduced. Summary of the Invention

[0006] (1) Technical Problem to be Solved

[0007] The object of the present invention is to propose a grid-adaptive simulation method for strong-shear turbulence coupled with the SA series model. By constructing a shear-layer adaptive subgrid length scale and introducing it into the initial region of the quasi-two-dimensional free shear layer, the subgrid length scale in the initial region of the free shear layer is effectively reduced, and the problem of high grid dependence of the existing RANS-LES hybrid model is overcome. While improving the computational accuracy, the computational cost is significantly reduced, the turbulence simulation process is significantly accelerated, and an effective numerical simulation method is provided for the low-cost and high-precision simulation of strong-shear flows in complex engineering flow problems. In addition, compared with the prior art, since the SA series model does not contain a turbulent kinetic energy term, the corresponding turbulent length scale cannot be obtained. The present invention aims to construct a new algebraic empirical formula to characterize the turbulent kinetic energy and the corresponding turbulent length scale, and thereby construct the SLA length scale to further improve the grid-adaptive performance.

[0008] (2) Technical Solution

[0009] To solve the above technical problem, the present invention provides a grid-adaptive simulation method for strong-shear turbulence coupled with the SA series model, including the following steps:

[0010] Step 1, determine whether to apply a shielding function;

[0011] Step 2, identify the shear-layer adaptive length scale;

[0012] Step 3, construct a scale-dependent adjustment function based on the turbulent energy spectrum integral;

[0013] Step 4, reconstruct the turbulent viscosity of the SA series model using the adjustment function;

[0014] Step 5, perform turbulence simulation using the reconstructed turbulent viscosity;

[0015] ① The determination of whether to apply a shielding function in Step 1 includes:

[0016] Judge whether to adopt the shielding function F in combination with the type of flow state simulated GAS , specifically, when the type of flow state is free shear flow, the shielding function is not adopted, and at this time the shielding function F GAS = 0; when the type of flow state is near-wall flow, the shielding function is adopted, and the shielding function F GAS Selectively use the F1 shielding function and F2 shielding function from the DDES-SST model and the F d shielding function from the DDES-SA model;

[0017] ② The identification of the shear layer adaptive length scale in step two includes:

[0018] Adopt the shielding function F in step one GAS to determine the local grid length scale Δ * ; the local grid length scale Δ * is given by the following formula:

[0019] Δ * = C GAS [(1 - F GAS )Δ SLA + F GAS Δ max

[0020]

[0021] Δ max = max(Δ x , Δ y , Δ z )

[0022]

[0023] where C GAS is an empirical coefficient, taking 0.6; Δ x is the length of the local hexahedral grid, Δ y is the width of the local hexahedral grid, Δ z is the height of the local hexahedral grid; is the distance from the cell center to the i-th vertex, is the unit normal vector of the vorticity vector, is the position vector of the cell vertex, is the position vector of the cell center;

[0024] Take values according to the following formula:

[0025]

[0026] ​wherein, is the strain rate tensor, is the vorticity vector, ω 2 is the square of the vorticity vector; θ takes 0.99, a1 = 0.15, a2 = 0.3; ν is the viscosity coefficient of the fluid, v t is the turbulent viscosity given by the SA series model, v t∞ is the far-field turbulent viscosity given by the SA series model;

[0027] <vtm>is the average value of the local VTM function value and the VTM function values of adjacent grids, F KH is based on the said <vtm>Two-segment linear function of values;

[0028] ③ The scale-dependent adjustment function constructed based on the integral of the turbulent energy spectrum described in Step 3 includes:

[0029] Based on the turbulent viscosity v given in the SA series model t and the velocity gradient tensor U ij , construct a new algebraic empirical formula to characterize the modeled turbulent kinetic energy k m as shown in the following formula:

[0030]

[0031] According to the local grid length scale Δ described in Step 2 * , obtain the actually modeled turbulent kinetic energy k through integration based on the turbulent energy spectrum u ; the actually modeled turbulent kinetic energy k u is obtained by the following formula:

[0032]

[0033] where E(κ) is the Kolmogorov turbulent energy spectrum, κ is the turbulent wave number, C k is the Kolmogorov constant coefficient, taking 1.5, ε is the actual turbulent dissipation rate, κ c is the resolvable turbulent truncation wave number, determined by the local grid length scale Δ described in Step 2 * :

[0034]

[0035] where π is the pi, taking 3.14;

[0036] According to the actually modeled turbulent kinetic energy k u , the modeled turbulent kinetic energy k m and the shielding function F described in Step 1 GAS , construct a dynamic scale-dependent adjustment function D f ; define the scale ratio as the ratio of the actually modeled turbulent kinetic energy k u and the modeled turbulent kinetic energy k m , and the dynamic scale-dependent adjustment function D f is a function related to the scale ratio, obtained by the following formula:

[0037]

[0038] l GAS =(1 - F GAS )l u +F GAS l m

[0039]

[0040] Among them, l u is the grid-related scale, and l m is the turbulence length scale given by the SA series of models and is obtained from the following formula:

[0041]

[0042] Among them, a0 is an empirical coefficient, taking 6.0;

[0043] ④ The reconstruction of the turbulence viscosity of the SA series of models using the adjustment function described in step four includes:

[0044] Adopt the dynamically scale-related adjustment function D f for the turbulence viscosity ν t in the SA series of models to perform regulation, and obtain the reconstructed turbulence viscosity ν sfs , which is obtained from the following formula:

[0045] ν sfs = D f ·ν t

[0046] ⑤ The turbulence simulation using the reconstructed turbulence viscosity described in step five includes:

[0047] Adopt the reconstructed turbulence viscosity ν sfs described in step four to calculate the Reynolds stress, update the mass, momentum, and energy transport equations of the SA series of models, and combine with the SA series of models to obtain the strong shear turbulence grid adaptive simulation method of the coupled SA series of models.

[0048] (III) Beneficial effects

[0049] A strong shear turbulence grid adaptive simulation method of a coupled SA series of models provided by the present invention has the following beneficial effects: by identifying the local grid size, combining the shear layer adaptive sub-grid length scale, determining the local grid length scale, and then reconstructing the turbulence viscosity through the integral of the turbulence energy spectrum to construct a scale-related function, grid adaptive simulation is realized, effectively improving the problems of large calculation cost and poor accuracy in the shear layer simulation of the RANS-LES hybrid simulation method, and significantly accelerating the turbulence simulation process.

[0050] Compared with the prior arts CN 117763838A and CN 117763995A, by introducing the SLA length scale, the method of the present invention significantly reduces the influence of the grid on the development of the shear layer, further improves the prediction accuracy of the grid-adaptive turbulence simulation method, effectively reduces the computational cost, and provides an important means for solving the problem of predicting strong-shear multi-scale complex flows in aeroengines.

[0051] The present invention has the characteristics of concise form and strong portability, can be well combined with various grid-adaptive turbulence simulations, is convenient to be implanted into existing CFD codes for application and expansion, has broad academic and engineering application prospects, and provides an effective numerical simulation method for low-cost and high-precision simulation of strong-shear flows in solving complex engineering flow problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 is a flowchart of a method for strongly-sheared turbulent grid adaptation simulation coupling the SA series models according to the present invention;

[0053] Figure 2 is a D f distribution cloud map based on the shear-layer adaptive subgrid length scale when the method for strongly-sheared turbulent grid adaptation simulation coupling the SA series models according to the present invention is applied to a specific example of a round-tube jet;

[0054] Figure 3 is a turbulent vortex structure diagram of a round-tube jet calculation example calculated using the original SA-noft2 model;

[0055] Figure 4 is a turbulent vortex structure diagram of a round-tube jet calculation example calculated using the method for strongly-sheared turbulent grid adaptation simulation coupling the SA series models according to the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0056] The following further describes in detail the specific embodiments of the present invention by taking the SA-noft2 model in the SA series models as an example and taking the round-tube jet flow as a calculation example in combination with the drawings and embodiments. The following embodiments are only used to illustrate the present invention, but not to limit the scope of the present invention.

[0057] The present invention provides a method for strongly-sheared turbulent grid adaptation simulation coupling the SA series models, including the following steps:

[0058] Step 1, determining whether to apply a shielding function;

[0059] In this step, in combination with the type of the simulated flow state, it is determined whether to adopt the shielding function F GAS , specifically, when the type of the flow state is free-shear flow, the shielding function is not adopted, and at this time the shielding function F GAS = 0; When the flow state type is near-wall flow, a shielding function is adopted, and the shielding function F GAS Selectively use the F1 shielding function and F2 shielding function from the DDES-SST model and the F from the DDES-SA model d Shielding function.

[0060] In the circular pipe jet example of the embodiment of the present invention, a high-quality hexahedral mesh is used for spatial discretization of the computational domain, and the total number of meshes is approximately 6.05 million.

[0061] In this embodiment, using the F from the IDDES-SA model B Function, then there is:

[0062] F GAS = F B

[0063] F B = min[2exp(-9α 2 ), 1.0]

[0064] α = 0.25 - d w / Δ max

[0065] Δ max = max(Δ x , Δ y , Δ z )

[0066] Among them, d w is the distance from the local mesh to the wall, and Δ x , Δ y , Δ z are the length, width, and height of the local hexahedral mesh respectively.

[0067] Step 2, identify the shear layer adaptive length scale;

[0068] In this step, the shielding function F GAS adopted in Step 1 is used to determine the local mesh length scale Δ * ; The local mesh length scale Δ * is given by the following formula:

[0069] Δ * = C GAS [(1 - F GAS )Δ SLA + F GAS Δ max )

[0070]

[0071] Δ max = max(Δ x , Δ y , Δ z )

[0072]

[0073] where C GAS is an empirical coefficient, taking 0.6; Δ x is the length of the local hexahedral mesh, Δ y is the width of the local hexahedral mesh, Δ z is the height of the local hexahedral mesh; is the distance from the cell center to the i-th vertex, is the unit normal vector of the vorticity vector, is the position vector of the cell vertex, is the position vector of the cell center;

[0074] takes values according to the following formula:

[0075]

[0076] where is the strain rate tensor, is the vorticity vector, ω 2 is the square of the said vorticity vector; θ takes 0.99, a1 = 0.15, a2 = 0.3; ν is the viscosity coefficient of the fluid, v t is the turbulent viscosity given by the SA series model, v t∞ is the far-field turbulent viscosity given by the SA series model.

[0077] The value range of the above VTM function is between 0 and 1. In the quasi-two-dimensional region at the initial stage of separation, the vorticity vector is also the eigenvector of the strain rate tensor , and at this time the VTM function value tends to 0; in the fully developed three-dimensional turbulence, the direction of the vorticity vector has a weak correlation with the eigenvector of the strain rate tensor , and at this time the VTM function value tends to 1.

[0078] <vtm>is the average value of the local VTM function value and the VTM function values of adjacent grids, F KH is based on <vtm>Two-segment linear function of the value. When <vtm>When the value is less than a certain threshold, the VTM function value is small; when <vtm>When the value gradually increases, the value of the VTM function rapidly increases to 1, thereby reducing the grid scale at the initial stage of separation. According to the sub-grid stress model, when the value of the VTM function increases to 1, the turbulent kinematic viscosity coefficient also decreases as expected.

[0079] Step three, construct a scale-dependent adjustment function based on the integration of the turbulent energy spectrum;

[0080] In this step, according to the turbulent viscosity v t and the velocity gradient tensor U ij given in the SA series models, a new algebraic empirical formula is constructed to characterize the modeled turbulent kinetic energy k m Taking the SA-noft2 turbulence model in the SA series models as an example in this embodiment, according to the turbulent viscosity v t and the velocity gradient tensor U ij given in the SA-noft2 turbulence model, a new algebraic empirical formula is constructed to characterize the modeled turbulent kinetic energy k m as shown in the following formula:

[0081]

[0082] According to the local grid length scale Δ * in step two, the actual turbulent kinetic energy k u to be modeled is obtained by integrating based on the turbulent energy spectrum; the actual turbulent kinetic energy k u to be modeled is obtained by the following formula:

[0083]

[0084] where E(κ) is the Kolmogorov turbulent energy spectrum, κ is the turbulent wave number, C k is the Kolmogorov constant coefficient, taking 1.5, ε is the actual turbulent dissipation rate, κ c is the resolvable turbulent cutoff wave number, which is determined by the local grid length scale Δ * in step two:

[0085]

[0086] where π is the pi, taking 3.14;

[0087] According to the actual turbulent kinetic energy k u to be modeled, the modeled turbulent kinetic energy k m and the shielding function F GAS in step one, a dynamic scale-dependent adjustment function D f is constructed, as Figure 2 shown.

[0088] Define the scale ratio as the actual turbulent kinetic energy k u and the modeled turbulent kinetic energy k m The ratio of the dynamically scaled adjustment function D f is a function related to the ratio of scales and is obtained from the following formula:

[0089]

[0090] l GAS =(1 - F GAS )l u + F GAS l m

[0091]

[0092] where l u is the grid-related scale, and l m is the turbulent length scale given by the SA series model and is obtained from the following formula:

[0093]

[0094] where a0 is an empirical coefficient and is taken as 6.0.

[0095] Step 4, use the adjustment function to reconstruct the turbulent viscosity of the SA series model;

[0096] In this step, the dynamically scaled adjustment function D f described in Step 3 is used to regulate the turbulent viscosity ν t in the SA series model to obtain the reconstructed turbulent viscosity ν sfs , which is obtained from the following formula:

[0097] ν sfs = D f ·ν t

[0098] In this embodiment, taking the SA-noft2 turbulent model in the SA series model as an example, the turbulent viscosity ν t in the SA-noft2 turbulent model is regulated to obtain the reconstructed turbulent viscosity ν sfs , which is obtained from the following formula:

[0099]

[0100] where ν is the viscosity coefficient of the fluid, is the turbulent viscosity directly obtained from the transport equation of the SA-noft2 turbulent model, and C ν1 is a constant coefficient in the SA-noft2 turbulent model and is taken as 7.1..

[0101] Step 5, use the reconstructed turbulent viscosity for turbulent simulation;

[0102] In this step, the reconstructed turbulent viscosity ν in Step 4 is adopted. sfs The Reynolds stress is calculated, and the mass, momentum, and energy transport equations of the SA series models are updated. Combining with the SA series models, the strong shear turbulent grid adaptive simulation method of the coupled SA series models is obtained. In this embodiment, taking the SA-noft2 turbulent model in the SA series models as an example, the reconstructed turbulent viscosity ν in Step 4 is adopted. sfs The Reynolds stress is calculated, and the mass, momentum, and energy transport equations of the SA-noft2 turbulent model are updated. Combining with the SA-noft2 turbulent model, the strong shear turbulent grid adaptive simulation method of the coupled SA series models is obtained and used for the numerical simulation of the round pipe jet example.

[0103] The transient calculation is carried out by adopting the fully implicit coupling solution technology, and the time step satisfies the CFL condition in engineering computational fluid dynamics. At the same time, the SA-noft2 turbulent model in the SA series models is selected to carry out the numerical simulation of the round pipe jet example of the embodiment of the present invention, and the numerical simulation results are compared with those of the strong shear turbulent grid adaptive simulation method of the coupled SA series models of the present invention.

[0104] Figure 3 It is the turbulent vortex structure diagram of the round pipe jet example calculated by using the SA-noft2 turbulent model in the SA series models, and the coloring is carried out by using the turbulent viscosity ratio.

[0105] Figure 4 It is the turbulent vortex structure diagram of the round pipe jet example calculated by using the strong shear turbulent grid adaptive simulation method of a coupled SA series model of the present invention, and the coloring is carried out by using the turbulent viscosity ratio.

[0106] Figure 3 、 Figure 4 The comparative analysis of shows that the analytical ability of the turbulent vortex structure obtained by using the strong shear turbulent grid adaptive simulation method of a coupled SA series model proposed by the present invention is stronger than that of the vortex structure calculated by the SA-noft2 turbulent model. Under the same number of grids, it can capture richer turbulent structures and provide more accurate flow field details.

[0107] The above is only the preferred embodiment of the patent of the present invention and is not used to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

[0108] To sum up, the strong shear turbulent grid adaptive simulation method of a coupled SA series model proposed by the present invention improves the local grid length scale Δ by identifying the local shear layer adaptive sub-grid length scale. * Recognition is further carried out by constructing a scale-related function through the integration of the turbulent energy spectrum to reconstruct the turbulent viscosity, realizing a more efficient grid adaptive simulation. This not only greatly reduces the computational cost and significantly speeds up the turbulent simulation process, but also constructs a grid length scale more suitable for strong shear layers, providing an efficient and low-cost numerical simulation method for the high-precision simulation of strong shear flows in complex engineering flow problems.< / vtm> < / vtm> < / vtm> < / vtm> < / vtm> < / vtm>

Claims

1. A grid adaptive simulation method for strongly sheared turbulence coupled with the SA series model, characterized in that, It includes the following steps: Step 1: Determine whether to apply a shielding function; Step 2: Identify the adaptive length scale of the shear layer; Step 3: Construct a scale-dependent adjustment function based on the integral of the turbulent energy spectrum; Step 4: Use the adjustment function to reconstruct the turbulent viscosity of the SA series model; Step 5: Use the reconstructed turbulent viscosity for turbulent simulation; ① The determination of whether to apply a shielding function described in Step 1 includes: Determine whether to use the shielding function F in combination with the simulated type of flow state GAS , specifically, when the type of flow state is free shear flow, the shielding function is not used, and at this time the shielding function F GAS = 0; when the type of flow state is near-wall flow, the shielding function is used, and the shielding function F GAS Selectively use the F1 shielding function, F2 shielding function from the DDES-SST model and the F d shielding function from the DDES-SA model; ② The identification of the adaptive length scale of the shear layer described in Step 2 includes: Adopt the shielding function F described in Step 1 GAS , to determine the local grid length scale Δ * ; the local grid length scale Δ * is given by the following formula: Δ * = C GAS [(1 - F GAS )Δ SLA + F GAS Δ max ​ Δ max = max(Δ x , Δ y , Δ z ) Among them, C GAS is an empirical coefficient, taking 0.6; Δ x is the length of the local hexahedral mesh, Δ y is the width of the local hexahedral mesh, Δ z is the height of the local hexahedral mesh; is the distance from the cell center to the i-th vertex, is the unit normal vector of the vorticity vector, is the position vector of the cell vertex, and r is the position vector of the cell center; Take values according to the following formula: Among them, is the strain rate tensor, ω is the vorticity vector, and ω 2 is the square of the vorticity vector; θ takes 0.99, a1 = 0.15, a2 = 0.3; ν is the viscosity coefficient of the fluid, and v t is the turbulent viscosity given by the SA series model, and v t∞ is the far-field turbulent viscosity given by the SA series model; <vtm>is the average value of the local VTM function value and the VTM function values of adjacent grids, F KH is based on the said <vtm>A two-segment linear function of the value;< / vtm> < / vtm> ③ The construction of a scale-dependent adjustment function based on the integral of the turbulent energy spectrum described in Step 3 includes: According to the turbulent viscosity ν given in the SA series model t and the velocity gradient tensor U ij , a new algebraic empirical formula is constructed to characterize the modeled turbulent kinetic energy k m as shown in the following formula: According to the local grid length scale Δ described in step two * , the turbulent kinetic energy k that should be actually modeled is obtained by integration based on the turbulent energy spectrum u ; the turbulent kinetic energy k that should be actually modeled u is obtained by the following formula: Among them, E(κ) is the Kolmogorov turbulence energy spectrum, κ is the turbulence wave number, and C k is the Kolmogorov constant coefficient, taking 1.5, ε is the actual turbulence dissipation rate, and κ c is the resolvable turbulence cut-off wave number, which is determined by the local grid length scale Δ * described in step two: where π is the pi, taking 3.14; According to the actual turbulent kinetic energy k to be modeled u , the modeled turbulent kinetic energy k m and the shielding function F described in step one GAS , construct a dynamic scale-dependent adjustment function D f ; define the scale ratio as the ratio of the actual turbulent kinetic energy k to be modeled u and the modeled turbulent kinetic energy k m , and the dynamic scale-dependent adjustment function D f is a function related to the scale ratio and is obtained from the following formula: l GAS = (1 - F GAS )l u + F GAS l m where l u is the grid-related scale, and l m is the turbulence length scale given by the SA series of models, which is obtained from the following formula: where a0 is an empirical coefficient, taking 6.0; ④ The reconstruction of the turbulent viscosity of the SA series model using the adjustment function described in Step 4 includes: Adopt the dynamic scale-related adjustment function D described in Step 3 f to regulate the turbulent viscosity ν in the SA series model t and obtain the reconstructed turbulent viscosity ν sfs , which is obtained from the following formula: ν sfs = D f · ν t ⑤ The use of the reconstructed turbulent viscosity for turbulent simulation described in Step 5 includes: Adopt the reconstructed turbulent viscosity ν described in step four sfs Calculate the Reynolds stress, update the mass, momentum, and energy transport equations of the SA series models, and combine them with the SA series models to obtain the strong shear turbulent grid adaptive simulation method for the coupled SA series models.

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