Fourth Order Accurate Finite Volume CWENO Scheme For Astrophysical MHD Problems

TL;DR

This paper introduces a simple, high-order finite volume scheme for astrophysical MHD problems that maintains magnetic field solenoidality and demonstrates high accuracy and robustness through various tests.

Contribution

It presents a fourth-order accurate finite volume CWENO scheme with constrained transport for astrophysical MHD on Cartesian meshes, combining high accuracy with robustness.

Findings

Achieves fourth-order accuracy in multiple tests.

Preserves magnetic field divergence-free condition to machine precision.

Demonstrates robustness in complex MHD simulations.

Abstract

In this work, a simple fourth-order accurate finite volume semi-discrete scheme is introduced to solve astrophysical magnetohydrodynamics (MHD) problems on Cartesian meshes. Hydrodynamic quantities like density, momentum and energy are discretised as volume averages. The magnetic field and electric field components are discretised as area and line averages respectively, so as to employ the constrained transport technique, which preserves the solenoidality of the magnetic field to machine precision. The present method makes use of a dimension-by-dimension approach employing a 1-D fourth-order accurate centrally weighted essentially non-oscillatory (1D-CWENO4) reconstruction polynomial. A fourth-order accurate, strong stability preserving (SSP) Runge-Kutta method is used to evolve the semi-discrete MHD equations in time. Higher-order accuracy of the scheme is confirmed in various linear and nonlinear multi-dimensional tests and the robustness of the method in avoiding unphysical numerical artifacts in the solution is demonstrated through several complex MHD problems.