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The Piecewise Parabolic Method for Multidimensional Relativistic Fluid Dynamics

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arxiv astro-ph/0505200 v1 pith:7EFTP5ZF submitted 2005-05-10 astro-ph

A. Mignone , T. Plewa , G. Bodo This is my paper
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keywords methodparabolicrelativisticaccurateapproximationdiscontinuitiesdynamicsequation
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We present an extension of the Piecewise Parabolic Method to special relativistic fluid dynamics in multidimensions. The scheme is conservative, dimensionally unsplit, and suitable for a general equation of state. Temporal evolution is second-order accurate and employs characteristic projection operators; spatial interpolation is piece-wise parabolic making the scheme third-order accurate in smooth regions of the flow away from discontinuities. The algorithm is written for a general system of orthogonal curvilinear coordinates and can be used for computations in non-cartesian geometries. A non-linear iterative Riemann solver based on the two-shock approximation is used in flux calculation. In this approximation, an initial discontinuity decays into a set of discontinuous waves only implying that, in particular, rarefaction waves are treated as flow discontinuities. We also present a new and simple equation of state which approximates the exact result for the relativistic perfect gas with high accuracy. The strength of the new method is demonstrated in a series of numerical tests and more complex simulations in one, two and three dimensions.

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