Summary: 
A Level Set Algorithm for Tracking
Discontinuities in Hyperbolic Conservation
Laws I: Scalar Equations
Tariq D. Aslam #
e­mail: aslam@lanl.gov
June 5, 1998
Abstract
A level set algorithm for tracking discontinuities in hyperbolic con­
servation laws is presented. The algorithm uses a simple finite di#er­
ence approach, analogous to the method of lines scheme presented in
[20]. The zero of a level set function is used to specify the location
of the discontinuity. Since a level set function is used to describe the
front location, no extra data structures are needed to keep track of the
location of the discontinuity. Also, two solution states are used at all
computational nodes, one corresponding to the ``real'' state, and one
corresponding to a ``ghost node'' state, analogous to the ``Ghost Fluid
Method'' of [6]. High order pointwise convergence is demonstrated for
linear and nonlinear conservation laws, even at discontinuities and in
multiple dimensions. The solutions are compared to standard high

Source: Aslam, Tariq - Los Alamos National Laboratory
California at Los Angeles, University of - Department of Mathematics, Group in Computational and Applied Mathematics

Collections: Mathematics; Physics