Preprint 1998-013

A Front Tracking Method for Conservation Laws with Boundary Conditions

Kenneth Hvistendahl Karlsen, Knut-Andreas Lie, and Nils Henrik Risebro

Abstract: A front tracking method is used to construct weak solutions to scalar conservation laws with two kinds of boundary conditions --- Dirichlet conditions and a novel zero flux (or no-flow) condition. The construction leads to an efficient numerical method. The main feature of the scheme is that there is no stability condition correlating the spatial and temporal discretization parameters. The analysis uses the traditional method of proving compactness via Helly's theorem as well as the more modern concept of measure valued solutions. Three numerical examples are presented.

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A front tracking method for conservation laws with boundary conditions
Kenneth Hvistendahl Karlsen, <>
Knut-Andreas Lie, <>
Nils Henrik Risebro, <>
Publishing information:
A MPEG-movie of the simulation in Example 3 is available. Moreover, we also provide a MPEG-movie of an oblique shock that interacts with 90 degree corner of a solid wall.
Submitted by:
<> March 30 1998.

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Last modified: Mon Mar 30 12:09:08 1998