Multidimensional Hall magnetohydrodynamics with isotropic or anisotropic thermal pressure: numerical scheme and its validation using solitary waves

Journal article

We present a numerical solver for plasma dynamics simulations in Hall magnetohydrodynamic (HMHD) approximation in one, two and three dimensions. We consider both isotropic and anisotropic thermal pressure cases, where a general gyrotropic approximation is used. Both explicit energy conservation equation and general polytropic state equations are considered. The numerical scheme incorporates second-order Runge-Kutta advancing in time and Kurganov-Tadmor scheme with van Leer flux limiter for the approximation of fluxes. A flux-interpolated constrainedtransport approach is used to preserve solenoidal magnetic field in the simulations. The implemented code is validated using several test problems previously described in the literature. Additionally, we propose a new validation method for HMHD codes based on solitary waves that provides a possibility of quantitative rigorous testing in nonlinear (large amplitude) regime as an extension to standard tests using small-amplitude whistler waves. Quantitative tests of accuracy and performance of the implemented code show the fidelity of the proposed approach.

Authors: Strumik, M; Stasiewicz, K

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Elsevier
• Journal: Journal of Computational Physics
• Volume: 330
• Pages: 846-862
• Publication date: 2016-10-01
• Acceptance date: 2016-10-25
• DOI: 10.1016/j.jcp.2016.10.058
• Keywords: anisotropic pressure; solitary waves; numerical methods; Hall magnetohydrodynamics