Foundations Of Computational Mathematics (FoCM 2005)

Workshop on Foundations of Numerical PDEs

July 7 - July 9, 2005

Universidad de Cantabria in Santander, Spain

Central-Upwind Schemes for Balance Laws. Applications to Multifluid and Multiphase Computations

Alexander Kurganov

Mathematics at Tulane University

Abstract:   First I will briefly describe Godunov-type central-upwind schemes for hyperbolic systems of conservation and balance laws. These schemes are simple, universal and, at the same time, high-resolution methods that can be applied as a `black-box' solver to many different problems. However, applications to balance laws typically require a special source term discretization, which should guarantee (a perfect) balance between the flux and the source terms. This will be illustrated on the example of the Saint Venant system of shallow water equations with nonflat bottom topography. Then I will focus on two more complicated applications: to compressible two-phase flows and to multi-layer shallow water equations, for which a treatment of nonconservative products seems to be the most challenging part in designing a reliable numerical method.