On GLM curl cleaning for a first order reduction of the CCZ4 formulation of the Einstein field equations

09/08/2019

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by   Michael Dumbser, et al.

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In this paper we propose an extension of the generalized Lagrangian multiplier method (GLM) of Munz et al. (JCP 2000, JCP 2002), which was originally conceived for the numerical solution of the Maxwell and MHD equations with divergence-type involutions, to the case of hyperbolic PDE systems with curl-type involutions. In particular, we apply the new method to a strongly hyperbolic first order reduction of the CCZ4 formulation (FO-CCZ4) of the Einstein field equations of general relativity. Several numerical examples, including the long-time evolution of a stable neutron star in anti-Cowling approximation, are presented in order to show the obtained improvements with respect to the standard formulation without special treatment of the curl involution constraints.