2024/02/06 by Tuan Anh Dao, Dao, Tuan Anh, Lukas Lundgren +3 · 1 citation
Engineering · Mathematics · #34A45 #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #G.1.8 #Gas Dynamics and Kinetic Theory #Nanofluid Flow and Heat Transfer #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2402.03929
openalex publication_date 2024/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Nonlinear conservation laws such as the system of ideal magnetohydrodynamics (MHD) equations may develop singularities over time. In these situations, viscous regularization is a common approach to regain regularity of the solution. In this paper, we present a new viscous flux to regularize the MHD equations which holds many attractive properties. In particular, we prove that the proposed viscous flux preserves positivity of density and internal energy, satisfies the minimum entropy principle, is consistent with all generalized entropies, and is Galilean and rotationally invariant. We also provide a variation of the viscous flux that conserves angular momentum. To make the analysis more useful for numerical schemes, the divergence of the magnetic field is not assumed to be zero. Using continuous finite elements, we show several numerical experiments including contact waves and magnetic reconnection.