An analytical solution of the isentropic vortex problem in the special relativistic magnetohydrodynamics

TL;DR

This paper derives an explicit analytical solution for the 2D and 3D isentropic vortex problem in special relativistic magnetohydrodynamics, improving upon previous numerical solutions used for testing numerical methods.

Contribution

It provides the first explicit algebraic analytical solutions for the isentropic vortex problem in special relativistic MHD, extending to 3D.

Findings

Analytical solutions for 2D and 3D cases are derived.

The solutions facilitate more accurate testing of numerical methods.

Extension from 2D to 3D is achieved explicitly.

Abstract

The isentropic vortex problem is frequently solved to test the accuracy of numerical methods and verify corresponding code. Unfortunately, its existing solution was derived in the relativistic magnetohydrodynamics by numerically solving an ordinary differential equation. This note provides an analytical solution of the 2D isentropic vortex problem with explicit algebraic expressions in the special relativistic hydrodynamics and magnetohydrodynamics and extends it to the 3D case.