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.

在开发 HALO3D（高海拔低轨道 3D）（一种用于高超声速流动的基于边缘的有限元方法多学科求解器）的背景下，本文介绍了具有外加磁场的流动模拟。应用低磁雷诺数近似，电流连续性方程用通过电导率张量引入的霍尔效应代替麦克斯韦方程。该方法通过模拟通过单对分段电极的电离流来验证。还介绍了在 21.38 马赫的半球上和在 17.61 马赫的 OREX（轨道再入实验）胶囊上的粘性电离流模拟。用于这些情况的 3D 非结构化混合网格使用基于解的 Hessian 的高度各向异性方法进行优化，结合多物理场适应标准，如密度、压力、温度、速度、湍流粘度和电势。与均匀网格细化或基于梯度的网格丰富不同，这种方法在不增加网格尺寸的情况下大大提高了精度。