Numerically Tracking Contact Discontinuities with an Introduction for GPU Programming

Davis, Sean L¹ 

[1]Los Alamos National Laboratory

关键词: ADVECTION;    ALGORITHMS;    COMPRESSION;    CONSERVATION LAWS;    FINITE DIFFERENCE METHOD;    IMPLEMENTATION;    PROGRAMMING;    STABILITY;    TRANSPORT;   

DOI  :  10.2172/1049332
RP-ID  :  LA-UR-12-24192
PID  :  OSTI ID: 1049332
Others  :  TRN: US201218%%199

学科分类：数学（综合）

美国|英语

来源: SciTech Connect

【 摘 要 】

We review some of the classic numerical techniques used to analyze contact discontinuities and compare their effectiveness. Several finite difference methods (the Lax-Wendroff method, a Multidimensional Positive Definite Advection Transport Algorithm (MPDATA) method and a Monotone Upstream Scheme for Conservation Laws (MUSCL) scheme with an Artificial Compression Method (ACM)) as well as the finite element Streamlined Upwind Petrov-Galerkin (SUPG) method were considered. These methods were applied to solve the 2D advection equation. Based on our results we concluded that the MUSCL scheme produces the sharpest interfaces but can inappropriately steepen the solution. The SUPG method seems to represent a good balance between stability and interface sharpness without any inappropriate steepening. However, for solutions with discontinuities, the MUSCL scheme is superior. In addition, a preliminary implementation in a GPU program is discussed.