A predictor–corrector symmetric TVD scheme for magnetogasdynamic flow

Abstract

In this paper, a predictor–corrector symmetric TVD scheme for nonlinear conservation laws is presented. The scheme does not necessitate the characteristic decomposition of the usual TVD schemes and employs component-wise limiting. We design two kinds of high accuracy flux limiters, obtain the TVD bounds and propose a hybrid approach. Then we apply it to solve magnetogasdynamic flow equations. A variety of test cases are provided, which are designed to test the robustness of the scheme and compare the results of both analytical and numerical results. According to the results, the new predictor–corrector symmetric TVD scheme is more accurate than two-step, component-wise TVD scheme (Yu and Liu, 2001) and explicit predictor–corrector TVD scheme (Xiaohua, 1990).