title: Conservative front tracking and level set algorithms.
abstract: Hyperbolic conservation laws are foundational for many branches of continuum physics. Discontinuities in the solutions of these partial differential equations are widely recognized as a primary difficulty for numerical simulation, especially for thermal and shear discontinuities and fluid-fluid internal boundaries. We propose numerical algorithms that will (i) track these discontinuities as sharp internal boundaries, (ii) fully conserve the conserved quantities at a discrete level, even at the discontinuities, and (iii) display one order of numerical accuracy higher globally (at the discontinuity) than algorithms in common use. A significant improvement in simulation capabilities is anticipated through use of the proposed algorithms.
authors.affiliation: Department of Applied Mathematics and Statistics, State University of New York, Stony Brook, NY 11794, USA. glimm@ams.sunysb.edu
authors.forename: J
authors.initials: J
authors.lastname: Glimm
authors.forename: X L
authors.initials: XL
authors.lastname: Li
authors.forename: Y
authors.initials: Y
authors.lastname: Liu
authors.forename: N
authors.initials: N
authors.lastname: Zhao