An improved estimate of the intermediate internal energy in the energy-consistent HLLD scheme
arXiv:2607.10293
The paper introduces a simple correction to the intermediate internal energy estimate in the HLLD approximate Riemann solver for magnetohydrodynamics, improving robustness and preserving pressure positivity even when magnetic fields are amplified by a factor of 1000.
Abstract
The robustness of approximate Riemann solutions has been a crucial topic in computational magnetohydrodynamics, from both theoretical and practical perspectives. Recently, the widely used HLLD approximate Riemann solution was revised, becoming significantly more robust under strong magnetic fields. Yet, simplifications were needed as the compressible slow magnetoacoustic mode is not included in the HLLD scheme, and as a result non-physical density distribution has been found when having strong slow shocks. In this note, a simple fix is introduced for the estimated intermediate internal energy, providing robust results in several representative test cases, preserving pressure-positivity when the magnetic field is enhanced by a factor of 1000.