Analysis of Second Order Time Filtered Backward Euler Method for MHD Equations

Abstract

The present work is devoted to introduce the backward Euler based modular time filter method for MHD flow. The proposed method improves the accuracy of the solution without a significant change in the complexity of the system. Since time filters for fluid variables are added as separate post processing steps, the method can be easily incorporated into an existing backward Euler code. We show that the time filtered backward Euler method delivers better correct energy and cross-helicity balance in comparison with the backward Euler method. Long-time stability, stability and second order convergence of the method are also proven. The influences of introduced time filter method on several numerical experiments are given, which both verify the theoretical findings and illustrate its usefulness on practical problems.