Performance of Geometric Multigrid Method for Two-Dimensional Burgers’Equations with Non-Orthogonal,Structured Curvilinear Grids

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.

An improved third-order HWCNS for compressible flow simulation on curvilinear grids

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.

Simulation of Seasonal Circulations and Thermohaline Variabilities in the Gulf of Thailand

Based on the Princeton Ocean Model （POM）, the seasonal thermohaline feature and the ocean circulation in the Gulf of Thailand （GOT）, situated between 6°N to 14°N latitude and 99°E to 105°E longitude, were studied numerically with 37 × 97 orthogonal curvilinear grid and 10 vertical sigma levels conforming to a realistic bottom topography. A spin-up phase of the first model run was executed using wind stress calculated from climatological monthly mean wind, restoring-type surface heat and salt, and climatological monthly mean fresh water flux data. In this paper, the temperature and salinity fields taken from Levitus94 data sets and the calculated temperature and salinity from the model run for 12-month mean and for each season are presented where the winter, summer, rainy, and end of the rainy seasons of Thailand are represented by the months January, April, July, and October, respectively. The simulated circulations are also described. The results show that the temperature in the GoT is warmer than the temperature of the other parts connected to the South China Sea （SCS）. At any depth of inflow from SCS into the GoT, the salinity is high, but in the outflow from the GoT at the surface, the salinity is low. The strong circulations are clockwise during summer and the rainy seasons of Thailand, which are the East Asian monsoon periods, northeasterly and southwesterly during summer. They occur near Pattani and Narathiwat provinces during summer and in the central GoT during the rainy seasons. Sensitivity experiments were designed to investigate the effects of wind forcing and open boundary conditions. Wind forcing is shown to be the important factor for generating the circulation in the GoT. The lateral velocity at the open boundaries is of considerable importance to current circulation for the rainy and end of the rainy seasons, with insignificant effect for the winter and summer seasons of Thailand.

A Stable Finite Difference Method for the Elastic Wave Equation on Complex Geometries with Free Surfaces

A stable and explicit second order accurate finite difference method for the elastic wave equation in curvilinear coordinates is presented.The discretization of the spatial operators in the method is shown to be self-adjoint for free-surface,Dirichlet and periodic boundary conditions.The fully discrete version of the method conserves a discrete energy to machine precision.