Two new high-order well-balanced schemes (CWENO finite difference on Cartesian grids and ADER DG on unstructured meshes) are proposed and validated for the Einstein-Euler system in generalized harmonic gauge, including stable long-term evolutions of Kerr black holes and perturbed neutron stars.
Well balanced finite volume methods for nearly hydrostatic flows.Journal of Computational Physics, 196(2):539–565, 2004
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High order numerical discretizations of the Einstein-Euler equations in the Generalized Harmonic formulation
Two new high-order well-balanced schemes (CWENO finite difference on Cartesian grids and ADER DG on unstructured meshes) are proposed and validated for the Einstein-Euler system in generalized harmonic gauge, including stable long-term evolutions of Kerr black holes and perturbed neutron stars.