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Subject: search.filters.subject.Chew–Goldberger–Low (CGL) plasma flow equations

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    Going beyond the MHD approximation: physics-based numerical solution of the CGL equations
    (IOP, 2024-07) Bhoriya, Deepak
    We present a new numerical model for solving the Chew–Goldberger–Low system of equations describing a bi-Maxwellian plasma in a magnetic field. Heliospheric and geospace environments are often observed to be in an anisotropic state with distinctly different parallel and perpendicular pressure components. The Chew–Goldberger–Low (CGL) system represents the simplest leading order correction to the common isotropic MHD model that still allows the incorporation of the latter’s most desirable features. However, the CGL system presents several numerical challenges: the system is not in conservation form, the source terms are stiff, and unlike MHD, it is prone to a loss of hyperbolicity if the parallel and perpendicular pressures become too different. The usual cure is to bring the parallel and perpendicular pressures closer to one another, but that has usually been done in an ad hoc manner. We present a physics-informed method of pressure relaxation based on the idea of pitch-angle scattering that keeps the numerical system hyperbolic and naturally leads to zero anisotropy in the limit of very large plasma beta. Numerical codes based on the CGL equations can, therefore, be made to function robustly for any magnetic field strength, including the limit where the magnetic field approaches zero. The capabilities of our new algorithm are demonstrated using several stringent test problems that provide a comparison of the CGL equations in the weakly and strongly collisional limits. This includes a test problem that mimics the interaction of a shock with a magnetospheric environment in 2D.
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    Entropy stable finite difference schemes for chew, goldberger and low anisotropic plasma flow equations
    (Springer, 2025-01) Bhoriya, Deepak
    In this article, we consider the Chew, Goldberger and Low (CGL) plasma flow equations, which is a set of nonlinear, non-conservative hyperbolic PDEs modeling anisotropic plasma flows. These equations incorporate the double adiabatic approximation for the evolution of the pressure, making them very valuable for plasma physics, space physics, and astrophysical applications. We first present the entropy analysis for the weak solutions. We then propose entropy-stable finite-difference schemes for the CGL equations. The key idea is to reformulate the CGL equations by rewriting some of the conservative terms in the non-conservation form. The conservative part of the reformulated equations is very similar to the magnetohydrodynamics (MHD) equations which is then symmetrized using Godunov’s symmetrization process for the MHD equations. The resulting equations are in the form where the conservative part combined with non-conservative Godunov’s terms is compatible with the entropy equation and the rest of the non-conservative terms do not contribute to the entropy equations. The final set of reformulated equations is then discretized by designing entropy conservative numerical flux and entropy diffusion operator based on the entropy scaled eigenvectors of the conservative part. We then prove the semi-discrete entropy stability of the schemes for the reformulated CGL equations. The schemes are then tested using several test problems derived from the corresponding MHD test cases.