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
Von Neumann stability theory is applied to analyze the stability of a fully coupled implicit(FCI)scheme based on the lower-upper symmetric Gauss-Seidel(LUSGS)method for inviscid chemical non-equilibrium flows.The FCI ...Von Neumann stability theory is applied to analyze the stability of a fully coupled implicit(FCI)scheme based on the lower-upper symmetric Gauss-Seidel(LUSGS)method for inviscid chemical non-equilibrium flows.The FCI scheme shows excellent stability except the case of the flows involving strong recombination reactions,and can weaken or even eliminate the instability resulting from the stiffness problem,which occurs in the subsonic high-temperature region of the hypersonic flow field.In addition,when the full Jacobian of chemical source term is diagonalized,the stability of the FCI scheme relies heavily on the flow conditions.Especially in the case of high temperature and subsonic state,the CFL number satisfying the stability is very small.Moreover,we also consider the effect of the space step,and demonstrate that the stability of the FCI scheme with the diagonalized Jacobian can be improved by reducing the space step.Therefore,we propose an improved method on the grid distribution according to the flow conditions.Numerical tests validate sufficiently the foregoing analyses.Based on the improved grid,the CFL number can be quickly ramped up to large values for convergence acceleration.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Von Neumann stability theory is applied to analyze the stability of a fully coupled implicit(FCI)scheme based on the lower-upper symmetric Gauss-Seidel(LUSGS)method for inviscid chemical non-equilibrium flows.The FCI scheme shows excellent stability except the case of the flows involving strong recombination reactions,and can weaken or even eliminate the instability resulting from the stiffness problem,which occurs in the subsonic high-temperature region of the hypersonic flow field.In addition,when the full Jacobian of chemical source term is diagonalized,the stability of the FCI scheme relies heavily on the flow conditions.Especially in the case of high temperature and subsonic state,the CFL number satisfying the stability is very small.Moreover,we also consider the effect of the space step,and demonstrate that the stability of the FCI scheme with the diagonalized Jacobian can be improved by reducing the space step.Therefore,we propose an improved method on the grid distribution according to the flow conditions.Numerical tests validate sufficiently the foregoing analyses.Based on the improved grid,the CFL number can be quickly ramped up to large values for convergence acceleration.
