The lower-upper symmetric Gauss-Seidel （LU-SGS） implicit relaxation has been widely used because it has the merits of less dependency on grid topology, low numerical complexity and modest memory requirements. In ori...The lower-upper symmetric Gauss-Seidel （LU-SGS） implicit relaxation has been widely used because it has the merits of less dependency on grid topology, low numerical complexity and modest memory requirements. In original LU-SGS scheme, the implicit system matrix is constructed based on the splitting of convective flux Jacobian according to its spectral radius. Although this treatment has the merit of reducing computational complexity and helps to ensure the diagonally dominant property of the implicit system matrix, it can also cause serious distortions on the implicit system matrix because too many approximations are introduced by this splitting method if the contravariant velocity is small or close to sonic speed. To overcome this shortcoming, an improved LU-SGS scheme with a hybrid construction method for the implicit system matrix is developed in this paper. The hybrid way is that： on the cell faces having small contravariant velocity or transonic contravariant velocity, the accurate derivative of the convective flux term is used to construct more accurate implicit system matrix, while the original Jacobian splitting method is adopted on the other cell faces to reduce computational complexity and ensure the diagonally dominant property of the implicit system matrix. To investigate the convergence performance of the improved LU-SGS scheme, 2D and 3D turbulent flows around the NACA0012 airfoil, RAE2822 airfoil and LANN wing are simulated on hybrid unstructured meshes. The nu- merical results show that the improved LU-SGS scheme is significantly more efficient than the original LU-SGS scheme.展开更多
We propose an efficient and robust algorithm to solve the steady Euler equa- tions on unstructured grids.The new algorithm is a Newton-iteration method in which each iteration step is a linear multigrid method using b...We propose an efficient and robust algorithm to solve the steady Euler equa- tions on unstructured grids.The new algorithm is a Newton-iteration method in which each iteration step is a linear multigrid method using block lower-upper symmetric Gauss-Seidel(LU-SGS)iteration as its smoother To regularize the Jacobian matrix of Newton-iteration,we adopted a local residual dependent regularization as the replace- ment of the standard time-stepping relaxation technique based on the local CFL number The proposed method can be extended to high order approximations and three spatial dimensions in a nature way.The solver was tested on a sequence of benchmark prob- lems on both quasi-uniform and local adaptive meshes.The numerical results illustrated the efficiency and robustness of our algorithm.展开更多
This paper proposes a stable and efficient implicit block Lower-Upper Symmetric-Gauss-Seidel(LU-SGS)algorithm-based lattice Boltzmann flux solver(LBFS)for simulation of hypersonic flows.In this method,the finite volum...This paper proposes a stable and efficient implicit block Lower-Upper Symmetric-Gauss-Seidel(LU-SGS)algorithm-based lattice Boltzmann flux solver(LBFS)for simulation of hypersonic flows.In this method,the finite volume method(FVM)is applied to discretize the Navier-Stokes equations,and the LBFS is utilized to evaluate the numerical flux at the cell interface.In LBFS,the local solution of discrete velocity Boltzmann equation(DVBE)with the non-free parameter D1Q4 lattice Boltzmann model is adopted to reconstruct the inviscid flux across the cell interface,and the viscous flux is approximated by conventional smooth function approach.In order to improve the robustness and convergence rate of the simulation for hypersonic flows,especially for problems with complex geometry,the implicit block LU-SGS algorithm is introduced to solve resultant discrete governing equations.A double cone model at Mach number of Ma=9.86 is firstly simulated to validate the proposed scheme,and a hypersonic flight vehicle with wings and rudders at Mach number of Ma=5.56 is then calculated to extend the application in practical engineering problems.Numerical results show that the proposed scheme could offer a more accurate and effective prediction for hypersonic flows.展开更多
In low speed flow computations,compressible finite-volume solvers are known to a)fail to converge in acceptable time and b)reach unphysical solutions.These problems are known to be cured by A)preconditioning on the ti...In low speed flow computations,compressible finite-volume solvers are known to a)fail to converge in acceptable time and b)reach unphysical solutions.These problems are known to be cured by A)preconditioning on the time-derivative term,and B)control of numerical dissipation,respectively.There have been several methods of A)and B)proposed separately.However,it is unclear which combination is the most accurate,robust,and efficient for low speed flows.We carried out a comparative study of several well-known or recently-developed low-dissipation Euler fluxes coupled with a preconditioned LU-SGS(Lower-Upper Symmetric Gauss-Seidel)implicit time integration scheme to compute steady flows.Through a series of numerical experiments,accurate,efficient,and robust methods are suggested for low speed flow computations.展开更多
基金Foundation item： National Natural Science Foundation of China （10802067）
文摘The lower-upper symmetric Gauss-Seidel （LU-SGS） implicit relaxation has been widely used because it has the merits of less dependency on grid topology, low numerical complexity and modest memory requirements. In original LU-SGS scheme, the implicit system matrix is constructed based on the splitting of convective flux Jacobian according to its spectral radius. Although this treatment has the merit of reducing computational complexity and helps to ensure the diagonally dominant property of the implicit system matrix, it can also cause serious distortions on the implicit system matrix because too many approximations are introduced by this splitting method if the contravariant velocity is small or close to sonic speed. To overcome this shortcoming, an improved LU-SGS scheme with a hybrid construction method for the implicit system matrix is developed in this paper. The hybrid way is that： on the cell faces having small contravariant velocity or transonic contravariant velocity, the accurate derivative of the convective flux term is used to construct more accurate implicit system matrix, while the original Jacobian splitting method is adopted on the other cell faces to reduce computational complexity and ensure the diagonally dominant property of the implicit system matrix. To investigate the convergence performance of the improved LU-SGS scheme, 2D and 3D turbulent flows around the NACA0012 airfoil, RAE2822 airfoil and LANN wing are simulated on hybrid unstructured meshes. The nu- merical results show that the improved LU-SGS scheme is significantly more efficient than the original LU-SGS scheme.
文摘We propose an efficient and robust algorithm to solve the steady Euler equa- tions on unstructured grids.The new algorithm is a Newton-iteration method in which each iteration step is a linear multigrid method using block lower-upper symmetric Gauss-Seidel(LU-SGS)iteration as its smoother To regularize the Jacobian matrix of Newton-iteration,we adopted a local residual dependent regularization as the replace- ment of the standard time-stepping relaxation technique based on the local CFL number The proposed method can be extended to high order approximations and three spatial dimensions in a nature way.The solver was tested on a sequence of benchmark prob- lems on both quasi-uniform and local adaptive meshes.The numerical results illustrated the efficiency and robustness of our algorithm.
文摘This paper proposes a stable and efficient implicit block Lower-Upper Symmetric-Gauss-Seidel(LU-SGS)algorithm-based lattice Boltzmann flux solver(LBFS)for simulation of hypersonic flows.In this method,the finite volume method(FVM)is applied to discretize the Navier-Stokes equations,and the LBFS is utilized to evaluate the numerical flux at the cell interface.In LBFS,the local solution of discrete velocity Boltzmann equation(DVBE)with the non-free parameter D1Q4 lattice Boltzmann model is adopted to reconstruct the inviscid flux across the cell interface,and the viscous flux is approximated by conventional smooth function approach.In order to improve the robustness and convergence rate of the simulation for hypersonic flows,especially for problems with complex geometry,the implicit block LU-SGS algorithm is introduced to solve resultant discrete governing equations.A double cone model at Mach number of Ma=9.86 is firstly simulated to validate the proposed scheme,and a hypersonic flight vehicle with wings and rudders at Mach number of Ma=5.56 is then calculated to extend the application in practical engineering problems.Numerical results show that the proposed scheme could offer a more accurate and effective prediction for hypersonic flows.
文摘In low speed flow computations,compressible finite-volume solvers are known to a)fail to converge in acceptable time and b)reach unphysical solutions.These problems are known to be cured by A)preconditioning on the time-derivative term,and B)control of numerical dissipation,respectively.There have been several methods of A)and B)proposed separately.However,it is unclear which combination is the most accurate,robust,and efficient for low speed flows.We carried out a comparative study of several well-known or recently-developed low-dissipation Euler fluxes coupled with a preconditioned LU-SGS(Lower-Upper Symmetric Gauss-Seidel)implicit time integration scheme to compute steady flows.Through a series of numerical experiments,accurate,efficient,and robust methods are suggested for low speed flow computations.
