Report 1999-03

The Method of Transport for the Euler Equations Written as a Kinetic Scheme

S.A. Zimmermann

Abstract: The Method of Transport is a genuinely multi-dimensional scheme to solve nonlinear systems of hyperbolic equations numerically. It is based on the framework of conservation laws. Here, we will consider the Euler equations. We will present an alternative formulation of the first order method based on kinetic theory. This will allow us to show that density and pressure of the numerical solution remain positive for all times. In addition, we can derive $L^1$-estimates for the numerical solution. We will also consider the second order method. This will give us more insight into the differences of the two formulations.

Keywords: Euler Equations, Multidimensional Schemes, Kinetic Schemes, Stability of Numerical Methods

Paper: Available as PDF (199 KB) or as hardcopy to order reports@sam.math.ethz.ch.

Publishing information: To appear in the Proceedings of the Seventh International Conference on Hyperbolic Problems, ETH Z\"urich, Febr. 9-13, 1998