CN-115906680-B - Implicit large vortex wall surface simulation method based on high-precision spectral element method and application thereof

CN115906680BCN 115906680 BCN115906680 BCN 115906680BCN-115906680-B

Abstract

The invention discloses an implicit large vortex wall simulation method based on a high-precision spectral element method, which is a method for constructing implicit large vortex simulation (SVV-iLES) based on a hp-type spectral element method and a SVV (SVV-vector) based on a spectral viscosity elimination method and realizing wall simulation under the framework of the method, and comprises the following steps of: according to the actual condition adjustment of the turbulent boundary layer, the corresponding points are ensured to fall in a logarithmic region, under the code frame of a spectral element method, interpolation processing is carried out on the unit speeds and the speeds u, the speed components parallel to the wall speeds are obtained and are substituted into an algebraic model, the wall stresses are obtained through analysis of the algebraic model, and finally the real-time modification of the boundary conditions of the logarithmic rate model is carried out to complete the simulation, so that the huge calculated amount caused by finer boundary layer grids in the flow problem is greatly reduced. The invention also provides an application of the simulation method in the high-Reynolds number wall flow scene, and an efficiency basis is provided for accurate calculation of flow.

Inventors

XU HUI
HUANG BOHUA
WANG RUI

Assignees

上海交通大学

Dates

Publication Date: 20260505
Application Date: 20220920

Claims (7)

1. An implicit large vortex simulation method based on a high-precision spectral element method, which is based on an hp-type spectral element method combined with a spectral viscosity elimination SVV to construct an implicit large vortex simulation method SVV-iLES, and a wall simulation method is added under the framework, which is characterized by comprising the following steps: S1, after N-order modes are reserved through a non-sticky Burgers equation expression, introducing an artificial SVV dissipative effect into a Fourier coefficient mathematical expression of a SVV kernel of a control equation, thereby defining an SVV operator, introducing the SVV operator into an NS equation, and further determining an SVV-iLES code frame; S2, in the turbulent boundary layer, the boundary layer is divided into a viscous bottom layer, a transition layer, a logarithmic rate layer and a boundary layer outer layer structure, the speed u at a corresponding position is obtained by setting the height h from the wall surface in a program, then the boundary layer is adjusted according to the actual condition of the turbulent boundary layer, the corresponding point is ensured to fall in a logarithmic region, and the unit speed is controlled under a code frame based on a spectral element method Interpolation processing is carried out on the velocity u; step S3, obtaining a speed component parallel to the wall surface speed on the basis of interpolation processing in the step S2; S4, substituting the velocity component in the step S3 into an algebraic model, obtaining wall stress through a Newton iteration method, taking the wall stress as a Newman wall boundary condition, simultaneously modifying the boundary condition in real time based on a turbulent boundary layer log rate model, setting the first layer grid height below a log rate layer, and setting the value of y+ to be more than 30; In the step S5, two algebraic models are used in the analysis of wall stress calculation, wherein the algebraic models adopt a traditional logarithmic rate expression or REICHARDT LAW expression.
2. The method for simulating the implicit large vortex wall surface based on the high-precision spectral element method according to claim 1, wherein in the step S1, under the corresponding initial and boundary conditions, the non-sticky Burgers equation expression is: The corresponding viscous solution expression is: Under the SVV method, N-order modes are reserved, and the expression of the above formula solution is: the fourier coefficient mathematical expression of the SVV kernel is: , , the method comprises the steps of performing Fourier expansion in a Fourier space, Only acts on the high wave number, Is a mapping operator which is used to map the data, Representing a convolution symbol, and defining that, in an initial operation, the wavenumber k is greater than P cut , Is 1, less than A value of 0, i.e. not functional, maday employs in the subsequent work 。
3. The method for simulating the implicit large vortex wall surface based on the high-precision spectral element method according to claim 2, wherein in the step S1, the SVV operator expression is: In the formula, Representing the effective dissipation intensity at discrete spectral elements.
4. The method for implicit large vortex wall simulation based on high-precision spectral element method according to claim 1, wherein in step S2, the unit speed is the same as that of the unit speed The interpolation formula is used for obtaining the following interpolation formula: wherein the speed is The method is composed of Lagrangian interpolation functions as basis functions, wherein u i is the corresponding coefficient of the basis functions; is a basis function within a cell.
5. The method for simulating an implicit large vortex wall surface based on high-precision spectral element method according to claim 4, wherein in step S2, the velocity u is obtained by the following interpolation formula: The calculation domain of the speed u is decomposed into hexahedral units, the speed field and the pressure field are expressed by Np order polynomials in each unit in the solving process, under a Cartesian coordinate system, when physical coordinates and corresponding unit IDs are in a linear relation, physical coordinate parameters are mapped to local coordinates in the unit IDs, wherein r, s, t and hi are one-dimensional Lagrangian polynomials.
6. The method for simulating an implicit large vortex wall surface based on high-precision spectral element method according to claim 1, wherein in step S3, the expression of the velocity component is: θ is the angle between the flow direction velocity and the wall surface.
7. The method for implicit large vortex wall surface simulation based on high-precision spectral element method according to claim 1, wherein in step S5, the logarithmic expression is, Wherein k=0.41, b=5.2; the expression REICHARDT LAW is that, Wherein d=9.8, e=1/11, f=1/3, k=0.41.

Description

Implicit large vortex wall surface simulation method based on high-precision spectral element method and application thereof Technical Field The invention belongs to the technical field of large vortex simulation, and particularly relates to an implicit large vortex wall surface simulation method based on a high-precision spectral element method and application thereof. Background In recent years, with the increase of computing power, more and more researchers have studied complex flow structures by high-precision numerical methods. The theoretical basis for the establishment of large vortex simulation is to eliminate small-scale vortices in high-Reynolds-number turbulence, and the large vortex simulation is also an important means in researching turbulent motion developed in more than ten years. The model adopted by the large vortex simulation is an explicit sub-lattice stress model generally, and a relatively small grid is required to be adopted, so that the calculation is complicated, analysis data is easy to make mistakes, and the related large vortex simulation method needs to be further improved. Because the high-precision format of the spectral element method has the characteristic of low dispersion dissipation, compared with the traditional low-order format, the spectral element method can be used for more accurately analyzing a complex flow structure, a SVV (singular value decomposition) based on spectral viscosity elimination method is provided for improving the stability of a classical Fourier spectrum method, SVV-iLES is constructed by combining the SVV and the spectral element method, and the calculation stability and accuracy can be effectively improved after verification, but in high-Reynolds number flow, the wall stress is difficult to accurately analyze by a thicker boundary layer grid, so that the difference between a calculation result and an actual result is larger, and if the thinner boundary layer grid is adopted, the required calculation amount is huge. Therefore, in order to further improve the calculation efficiency in the high Reynolds number flow application scene, we add a wall model in the implicit large vortex simulation (SVV-iLES) based on the spectral element method, continue to base on the high-precision hp-type spectral element method with good dispersion, geometric adaptability and dissipation characteristics, and meanwhile, the modeling processing can be carried out for the complex turbulence problem in the massive parallel environment due to the strong parallel expandability, and reliable numerical results can be provided for analysis. Disclosure of Invention The invention aims to solve the problems and provide an implicit large vortex wall surface simulation method based on a high-precision spectral element method and application thereof, so as to conveniently solve the problem of complex turbulence and improve the calculation precision and efficiency. The invention has the technical scheme that the implicit large vortex wall surface simulation method based on the high-precision spectral element method is a method for constructing SVV-iLES based on the hp-type spectral element method and combining SVV by an viscosity elimination method and realizing wall surface simulation under the frame of the SVV-iLES, and is characterized by comprising the following steps: and (1) introducing an artificial SVV dissipative effect into a Fourier coefficient mathematical expression of a SVV kernel of a control equation after retaining an N-order mode through a non-sticky Burgers equation expression, thereby defining an SVV operator, introducing the SVV operator into an NS equation, and further determining an SVV-iLES code frame. In the step (2), in a turbulent boundary layer, the method is divided into a viscous bottom layer, a transition layer, a logarithmic rate layer and a boundary layer outer layer structure, the speed u at a corresponding position is obtained by setting the height h from a wall surface in a program, then the speed u is adjusted according to actual conditions, the corresponding point is ensured to fall in a logarithmic region, and interpolation processing is carried out on the unit speed u (x) and the speed u under a code frame based on a spectral element method. And (3) obtaining a speed component parallel to the wall speed on the basis of the interpolation processing of the step (2). And (4) substituting the velocity component in the step (3) into an algebraic model, obtaining wall stress through a Newton iteration method, taking the wall stress as a Newman wall boundary condition, simultaneously modifying the boundary condition in real time based on a turbulent boundary layer log rate model, setting the first layer grid height in a log rate layer, and setting the value of y+ to be more than 30 generally. In the step (5), in the analysis of wall stress calculation, two algebraic models are used, and a traditional logarithmic rate expression or REICHARDT LAW expre