# Numerical analysis of an efficient second order time filtered backward Euler method for MHD equations

## TL;DR

This paper introduces a second-order time filtering method based on backward Euler for MHD equations, enhancing accuracy and stability with minimal additional complexity, and verified through numerical experiments.

## Contribution

The paper presents a novel modular time filter for backward Euler that improves accuracy and stability in MHD simulations without significant computational overhead.

## Key findings

- The method achieves second-order convergence.
- It maintains long-term stability and conservation properties.
- Numerical experiments confirm theoretical results and practical usefulness.

## 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 investigate the conservation and long time stability properties of the improved scheme. 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.