Report 1997-13

The Method of Transport for mixed hyperbolic-parabolic systems

J. Maurer

Abstract: Starting from a numerical scheme for solving systems of hyperbolic partial differential equations the transition to parabolic equations of the type of advection-diffusion equations needs a different treatment of the viscous part. Since we are using a genuine multi-dimensional scheme also the fact that the diffusion acts in infinitely many directions shall be captured properly. Therefore, to be able to use this scheme we have developed a decomposition of the scalar advection-diffusion equation into a special system of advection equations. In particular the interaction of the advection and diffusion part will be taken into account. The extension to the Navier-Stokes equations which are a system of mixed hyperbolic-parabolic type is possible and will be pointed out.

Keywords: Finite Volume Schemes, Hyperbolic Conservation Laws, Numerical Viscosity, Euler Equations, Advection-Diffusion Equation, Navier-Stokes Equations

Paper: Available as PDF (541 KB) or as hardcopy to order reports@sam.math.ethz.ch.