This paper seeks to develop an efficient multigrid algorithm for solving the Burgers problem with the use of non-orthogonal structured curvilinear grids in L-shaped geometry.For this,the differential equations were di...This paper seeks to develop an efficient multigrid algorithm for solving the Burgers problem with the use of non-orthogonal structured curvilinear grids in L-shaped geometry.For this,the differential equations were discretized by Finite Volume Method(FVM)with second-order approximation scheme and deferred correction.Moreover,the algebraic method and the differential method were used to generate the non-orthogonal structured curvilinear grids.Furthermore,the influence of some parameters of geometric multigrid method,as well as lexicographical Gauss–Seidel(Lex-GS),η-line Gauss–Seidel(η-line-GS),Modified Strongly Implicit(MSI)and modified incomplete LU decomposition(MILU)solvers on the Central Processing Unit(CPU)time was investigated.Therefore,several parameters of multigrid method and solvers were tested for the problem,with the use of nonorthogonal structured curvilinear grids and multigrid method,resulting in an algorithm with the combination that achieved the best results and CPU time.The geometric multigrid method with Full Approximation Scheme(FAS),V-cycle and standard coarsening ratio for this problem were utilized.This article shows how to calculate the coordinates transformation metrics in the coarser grids.Results show that the MSI and MILU solvers are the most efficient.Moreover,theMSI solver is faster thanMILU for both grids generators;and the solutions are more accurate for the Burgers problem with grids generated using elliptic equations.展开更多
The method of automatically generating generalized curvilinear meshes has many advantages and is beginning to be used in ocean simulations. This three dimensional (3 D) coastal barotropic model in generalized curvilin...The method of automatically generating generalized curvilinear meshes has many advantages and is beginning to be used in ocean simulations. This three dimensional (3 D) coastal barotropic model in generalized curvilinear grids was developed to simulate the M 2, S 2, K 1 and O 1 tidal waves in the Bohai Sea, China. The numerical results agreeing with observations showed that the method is an effective tool for improving accuracy of simulations in shallow shelf seas, especially in the near coast region, if the pseudo effect there usually caused by rectangular grids can be removed.展开更多
Due to the very high requirements on the quality of computational grids,stability property and computational efficiency,the application of high-order schemes to complex flow simulation is greatly constrained.In order ...Due to the very high requirements on the quality of computational grids,stability property and computational efficiency,the application of high-order schemes to complex flow simulation is greatly constrained.In order to solve these problems,the third-order hybrid cell-edge and cell-node weighted compact nonlinear scheme(HWCNS3)is improved by introducing a new nonlinear weighting mechanism.The new scheme uses only the central stencil to reconstruct the cell boundary value,which makes the convergence of the scheme more stable.The application of the scheme to Euler equations on curvilinear grids is also discussed.Numerical results show that the new HWCNS3 achieves the expected order in smooth regions,captures discontinuities sharply without obvious oscillation,has higher resolution than the original one and preserves freestream and vortex on curvilinear grids.展开更多
文摘This paper seeks to develop an efficient multigrid algorithm for solving the Burgers problem with the use of non-orthogonal structured curvilinear grids in L-shaped geometry.For this,the differential equations were discretized by Finite Volume Method(FVM)with second-order approximation scheme and deferred correction.Moreover,the algebraic method and the differential method were used to generate the non-orthogonal structured curvilinear grids.Furthermore,the influence of some parameters of geometric multigrid method,as well as lexicographical Gauss–Seidel(Lex-GS),η-line Gauss–Seidel(η-line-GS),Modified Strongly Implicit(MSI)and modified incomplete LU decomposition(MILU)solvers on the Central Processing Unit(CPU)time was investigated.Therefore,several parameters of multigrid method and solvers were tested for the problem,with the use of nonorthogonal structured curvilinear grids and multigrid method,resulting in an algorithm with the combination that achieved the best results and CPU time.The geometric multigrid method with Full Approximation Scheme(FAS),V-cycle and standard coarsening ratio for this problem were utilized.This article shows how to calculate the coordinates transformation metrics in the coarser grids.Results show that the MSI and MILU solvers are the most efficient.Moreover,theMSI solver is faster thanMILU for both grids generators;and the solutions are more accurate for the Burgers problem with grids generated using elliptic equations.
文摘The method of automatically generating generalized curvilinear meshes has many advantages and is beginning to be used in ocean simulations. This three dimensional (3 D) coastal barotropic model in generalized curvilinear grids was developed to simulate the M 2, S 2, K 1 and O 1 tidal waves in the Bohai Sea, China. The numerical results agreeing with observations showed that the method is an effective tool for improving accuracy of simulations in shallow shelf seas, especially in the near coast region, if the pseudo effect there usually caused by rectangular grids can be removed.
基金supported by the Basic Research Foundation of the National Numerical Wind Tunnel Project(Grant No.NNW2018-ZT4A08)the National Key Project(Grant No.GJXM92579)of China.
文摘Due to the very high requirements on the quality of computational grids,stability property and computational efficiency,the application of high-order schemes to complex flow simulation is greatly constrained.In order to solve these problems,the third-order hybrid cell-edge and cell-node weighted compact nonlinear scheme(HWCNS3)is improved by introducing a new nonlinear weighting mechanism.The new scheme uses only the central stencil to reconstruct the cell boundary value,which makes the convergence of the scheme more stable.The application of the scheme to Euler equations on curvilinear grids is also discussed.Numerical results show that the new HWCNS3 achieves the expected order in smooth regions,captures discontinuities sharply without obvious oscillation,has higher resolution than the original one and preserves freestream and vortex on curvilinear grids.
