 
Summary: A Level Set Algorithm for Tracking
Discontinuities in Hyperbolic Conservation
Laws I: Scalar Equations
Tariq D. Aslam
email: aslam@lanl.gov
June 8, 1998
Abstract
A level set algorithm for tracking discontinuities in hyperbolic con
servation laws is presented. The algorithm uses a simple finite differ
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
order shock capturing schemes. This paper focuses on scalar conser
