TP-32

Flow-Field Dependent Variation Method: Capturing Relativistic Shock Waves to Instrument Design

G. A. Richardson¹, T. J. Chung², G. R. Karr², G. N. Pendleton¹,³¹Center for Space Plasma, Aeronomical, and Astrophysical Research, University of Alabama - Huntsville ²Department of Mechanical and Aerospace Engineering, University of Alabama - Huntsville ³Department of Physics, University of Alabama - Huntsville

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 discuss traditional methods used in astrophysics problems, their pros and cons, and how new methods can help in the advancement of this field. In particular we will present the flow-field dependent variation (FDV) method to accurately solve very high-speed problems, as well as capture relativistic shocks, all while allowing the user to apply their familiar FDM or FEM solver. This method is also versatile enough to apply the non-relativistic Navier-Stokes equations to solve low speed and even convection free problems making it useful in instrument design. In the FDV method, numerical schemes are automatically adjusted from the current flowfield information reflecting shock discontinuities and/or effects of viscosity in boundary layers. To demonstrate the validity of this theory, some application problems using the relativistic hydrodynamic equations will be presented as well as applications to difficult heat flow problems that arise during instrument development.