Validation Test Cases for Multi-Physic Problems: Application to Magneto-Hydrodynamic Numerical Simulations

TL;DR

This paper develops and analyzes elementary test cases for laminar magneto-hydrodynamic flows, providing analytical solutions and insights into the physics, especially relevant for MHD propulsion applications.

Contribution

It introduces analytical solutions for key MHD flow problems and discusses their implications for magneto-hydrodynamic simulation validation.

Findings

Analytical solutions for Hartmann, Couette, and Rayleigh flows with magnetic forcing.

Identification of key non-dimensional numbers governing the physics.

Insights into MHD propulsion through nozzle flow analysis.

Abstract

In the present paper, some elementary test cases in laminar flow with magnetic forcing terms are analyzed (Hartmann flow, Couette flow, Rayleigh flow); equations of the coupled problem are exposed and analytical solutions are derived in each case, highlighting the relevant non-dimensional number which drives the physics of the problem. Several analytical calculations are then proposed and discussed, in particular in the context of MHD propulsion by a nozzle.