Flow-field dependent variation method for complex relativistic fluids

Abstract

Many current high-energy astrophysics problems, particularly those containing shock waves and high-speed flow, do not take advantage of new computational fluid dynamics (CFD) techniques available in such fields as aerospace engineering. We will present the flow-field dependent variation (FDV) method to accurately solve very high-speed flow problems, as well as capture relativistic shocks, all while allowing the user to apply their familiar finite difference method (FDM) or finite element method (FEM). This method is also versatile enough to apply the non-relativistic Naiver-Stokes equations to solve low speed flows. In the FDV method, numerical schemes are automatically adjusted from the current flow field information reflecting shock discontinuities and/or effects of viscosity in boundary layers. To demonstrate the validity of this theory, the shock tube using the relativistic hydrodynamic equations has been applied.