Excision methods for high resolution shock capturing schemes applied to general relativistic hydrodynamics

High-Order Residual Distribution Schemes for Steady 1D Relativistic Hydrodynamics

An important goal in astrophysics is to model phenomena such as the gravitational collapse of stars and accretion onto black holes. Under the assumption that the spacetime metric remains fixed on the time scales of fluid motion, the relevant physics can be modeled by the equations of relativistic hydrodynamics. These equations form a system of hyperbolic balance laws that are strongly nonlinear...

Flux-gradient and Source Term Balancing for Certain High Resolution Shock-capturing Schemes

We present an extension of Marquina’s flux formula, as introduced in [8], for the shallow water system. We show that the use of two different Jacobians at cell interfaces prevents the scheme from satisfying the exact C-property [2] while the approximate C-property is satisfied for higher order versions of the scheme. The use of a single Jacobian in Marquina’s flux splitting formula leads to a n...

A Class of High Resolution Shock Capturing Schemes for Non-linear Hyperbolic Conservation Laws

Abstract. A general procedure to construct a class of simple and efficient high resolution Total Variation Diminishing (TVD) schemes for non-linear hyperbolic conservation laws by introducing anti-diffusive terms with the flux limiters is presented. In the present work the numerical flux function for space discretization is constructed as a combination of numerical flux function of any entropy ...

High- Resolution Shock-Capturing Schemes for Inviscid and Viscous Hypersonic Flows

High-order TVD shock-capturing schemes for unstructured grid solvers