MHD-A: A Fluctuation Splitting Wave Model for Planar Magnetohydrodynamics

Here we present MHD-A, a two-dimensional (2D) upwind residual distribution (fluctuation splitting) scheme designed for solving planar magnetohydrodynamics (MHD) equations on both structured and unstructured triangular meshes. This scheme operates at second-order accuracy in both space and time, using a consistent 2D wave model derived from the eigensystem of the MHD flux vector's Jacobian matrix. It handles entropy, magnetoacoustic, and numerical magnetic monopole waves, but not Alfven waves due to the planar nature of the problem. Notably, wave propagation directions are determined solely by flow properties and field gradients, unaffected by mesh structure. Additionally, this scheme achieves second-order accuracy without requiring flux evaluations or neighboring cell data. Testing has shown MHD-A delivers promising results, marking it as the first fluctuation splitting wave model for multidimensional MHD.