Scientific Computing Group Seminars - Detail View

Speaker: M. Ben-Artzi

Affiliation: Hebrew University

Talk Title: Conservation laws on a manifold

Invited by: Chi-Wang Shu

Time: Oct. 17 2008 11 a.m.

Location: 182 George Street, Room 110

Abstract:

The basic model of atmospheric flow is the "Shallow-Water" system (on the sphere). It is a complicated system of nonlinear hyperbolic equations, involving material discontinuities, shocks and other wave patterns. The aim of this talk is an attempt to deal with some features (theoretical and computational) of the system by using a simplified scalar model, namely, a class of nonlinear scalar hyperbolic equations on surfaces. They are the "geometric" equivalents of the famous Burgers equation. The theory of existence and uniqueness is stated (uniqueness is implied by a suitable version of the entropy condition). A numerical finite-volume scheme is introduced (generalization of the Godunov method). Its convergence can be demonstrated (for the first-order version). Some numerical results are presented, showing a very rich collection of steady-state solutions, solutions confined to designated domains and more. (Joint work with J. Falcovitz and Ph. LeFloch).