Edge-Based Finite Element Formulation of Magnetohydrodynamics at High Mach Numbers

Abstract

In the context of the development of HALO3D (High Altitude Low Orbit 3D), an edge-based Finite Element Method multidisciplinary solver for hypersonic flows, this paper presents the simulation of flows with an imposed magnetic field. Applying the low-magnetic Reynolds number approximation, a current-continuity equation replaces Maxwell's equations with the Hall effect introduced through an electrical conductivity tensor. The approach is validated via the simulation of ionized flow through singly-paired segmented electrodes. Viscous, ionized flow simulations over a hemisphere at Mach 21.38 and over the OREX (Orbital Re-entry Experiment) capsule at Mach 17.61 are also presented. The 3D unstructured hybrid meshes used for these cases are optimized with a highly anisotropic methodology based on the Hessians of the solution, combining multi-physics adaptation criteria such as density, pressure, temperature, velocity, turbulent viscosity and electric potential. Unlike uniform mesh refinement or gradient-based mesh enrichment, this approach greatly improves accuracy without increasing mesh size.