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Flux Limiter Methods in 3D Numerical Relativity

C. Bona·C. Palenzuela
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Abstract

New numerical methods have been applied in relativity to obtain a numerical evolution of Einstein equations much more robust and stable. Starting from 3+1 formalism and with the evolution equations written as a FOFCH (first-order flux conservative hyperbolic) system, advanced numerical methods from CFD (Computational Fluid Dynamics) have been successfully applied. A flux limiter mechanism has been implemented in order to deal with steep gradients like the ones usually associated with black hole spacetimes. As a test bed, the method has been applied to 3D metrics describing propagation of nonlinear gauge waves. Results are compared with the ones obtained with standard methods, showing a great increase in both robustness and stability of the numerical algorithm.

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C. Bona, C. Palenzuela. 2002-02-28. Flux Limiter Methods in 3D Numerical Relativity. https://doi.org/10.1007/3-540-36973-2_7

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