A high order finite difference solver for simulations of turbidity currents with high parallel efficiency

Abstract

We present a high order finite difference solver, ParaTC , for the direct numerical simulations of turbidity currents with canonical turbulent channel configuration (periodic boundary conditions in the horizontal directions and non-periodic in vertical direction). Uniform meshes are adopted in streamwise and spanwise directions, while stretched grids can be used in wall-normal direction. In order to improve the parallel efficiency, we propose a new 2D pencil-like parallel configuration with totally 6 different pencil arrangements. A parallel Thomas algorithm is also included to further reduce the communication overhead when solving tridiagonal equations. In addition, we perform an optimal search method in the initializing stage to find the fastest Poisson solver scheme among four alternatives for a specific mesh configuration. The runtime ratio between traditional pencil-like Poisson solver and present solver is about 1.5. An approximate linear strong scaling performance is achieved, and the weak scaling performance is also improved. Three benchmark simulations are preformed, and the statistics are compared with those extracted from the simulations by the spectral method, and good agreements are achieved. The source code is freely available at https://github.com/GongZheng-Justin/ParaTC .