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When

Start: 10/23/2013 - 1:15pm

End : 10/23/2013 - 2:15pm

End : 10/23/2013 - 2:15pm

Category

Applied Math Seminar

Speaker

Alexander Kurganov (Tulane University)

Abstract

I will first give a brief description of finite-volume, Godunov-type methods for hyperbolic

systems of conservation laws. These methods consist of two types of schemes: upwind and

central. My lecture will focus on the second type -- non-oscillatory central schemes.

Godunov-type schemes are projection-evolution methods. In these methods, the solution, at

each time step, is interpolated by a (discontinuous) piecewise polynomial interpolant, which

is then evolved to the next time level using the integral form of conservation laws. Therefore,

in order to design an upwind scheme, (generalized) Riemann problems have to be

(approximately) solved at each cell interface. This however may be hard or even impossible.

The main idea in the derivation of central schemes is to avoid solving Riemann problems by

averaging over the wave fans generated at cell interfaces. This strategy leads to a family of

universal numerical methods that can be applied as a black-box-solver to a wide variety of

hyperbolic PDEs and related problems. At the same time, central schemes suffer from

(relatively) high numerical viscosity, which can be reduced by incorporating of some

upwinding information into the scheme derivation -- this leads to central-upwind schemes,

which will be presented in the lecture.

During the talk, I will show a number of recent applications of the central schemes.

Where

Davidson, CMC