TY - JOUR
T1 - A Provably Positive-Preserving HLLD Riemann Solver for Ideal Magnetohydrodynamics. Part I: The One-Dimensional Case
AU - Zhang , Xiaoteng
AU - Wang , Xun
AU - Shen , Zhijun
AU - Yang , Chao
JO - Communications in Computational Physics
VL - 4
SP - 1120
EP - 1156
PY - 2025
DA - 2025/04
SN - 37
DO - http://doi.org/10.4208/cicp.OA-2024-0068
UR - https://global-sci.org/intro/article_detail/cicp/24033.html
KW - Approximate Riemann solver, positivity-preserving method, multi-moment constrained finite volume method, arbitrary-Lagrangian-Eulerian (ALE) framework.
AB - <p style="text-align: justify;">Combining robustness and high accuracy is one of the primary challenges
in the magnetohydrodynamics (MHD) field of numerical methods. This paper investigates two critical physical constraints: wave order and positivity-preserving (PP) properties of the high-resolution HLLD Riemann solver, which ensures the positivity of
density, pressure, and internal energy. This method’s distinctiveness lies in its ability
to ensure that the wave characteristic speeds of the HLLD Riemann solver are strictly
ordered. A provably PP HLLD Riemann solver based on the Lagrangian setting is established, which can be viewed as an extension of the PP Lagrangian method in hydrodynamics but with more and stronger constraint condition. In addition, the above two
properties are ensured on moving grid method by employing the Lagrange-to-Euler
transform. Meanwhile, a novel multi-moment constrained finite volume method is
introduced to acquire third order accuracy, and practical limiters are applied to avoid
numerical oscillations. Selected numerical benchmarks demonstrate the robustness
and accuracy of our methods.</p>