The discontinous Galerkin method applied on the equations of ideal relativistic hydrodynamics

Details The discontinous Galerkin method applied on the equations of ideal relativistic hydrodynamics The discontinous Galerkin method applied on the equations of ideal relativistic hydrodynamics

Jul 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002phdt.........3s&link_type=abstract

PhD Thesis, Naturwissenschaftlich-Mathematische Gesamtfakultät der Universität Heidelberg, Germany. 79 pp. (2002)

Statistics

Computation

2

Relativistic Hydrodynamics, Relativistic Jets, Accretion Disks

Scientific paper

To solve numerically the problems of ideal relativistic hydrodynamics we have developed a high-order accurate and time-explicit code. For the spatial discretisation we use the Discontinuous Galerkin Method (DGM), which is a sub-class of the Finite Element Methods (FEM). The DG methods are numerically stable for advection-dominated problems and a high-order of spatial accuracy is reachable, even by using unstructured meshes for the discretisation of a computational domain. A higher formal accuracy is easily achieved by using a higher-order Finite Element basis. Further, an efficient parallelisation of the DG method is possible, due to their compact form. This code was able to solve the standard test-problems of the Newtonian and relativistic hydrodynamics in one and two dimensions with high accuracy. The effective resolution reached in the computation is comparable to that of the modern High Resolution Shock Capturing (HRSC) methods. In addition, we applied the code to astrophysical problems of interest, a jet propagating in a homogeneous media and relativistic accretion disc of black holes.

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