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Erschienen in:
2009 | OriginalPaper | Buchkapitel
The ADER Approach
verfasst von : Eleuterio F. Toro
Erschienen in: Riemann Solvers and Numerical Methods for Fluid Dynamics
Verlag: Springer Berlin Heidelberg
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This chapter is an introduction to the ADER family of fully–discrete, one–step methods of arbitrary order of accuracy in space and time, for solving hyperbolic equations with source terms. These schemes are a generalization of the Godunov method. The numerical flux is computed as a time–integral average of the flux function evaluated at the solution of the generalized Riemann problem studied in chapter 19, and the numerical source is computed as a high–order space-time integral of the source term in the appropriate control volume. The ADER approach operates in the framework of finite volumes and of discontinuous Galerkin finite elements. Here we deal with the finite volume framework for one-dimensional model problems.