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The Derivative Riemann Problem: The Basis for High Order ADER Schemes

Toro, E., M. Dumbser, V. Titarev, and M. Käser (2006), The Derivative Riemann Problem: The Basis for High Order ADER Schemes, in Proceedings of the European Conference on Computational Fluid Dynamics, ECCOMAS, Delft.

Abstract
The corner stone of arbitrary high order schemes (ADER schemes) is the solution of the derivative Riemann problem at the element interfaces, a generalization of the classical Riemann problem first used by Godunov in 1959 to construct a first-order upwind numerical method for hyperbolic systems. The derivative Riemann problem extends the possible initial conditions to piecewise smooth functions, separated by a discontinuity at the interface. In the finite volume framework, these piecewise smooth functions are obtained from cell averages by a high order non-oscillatoryWENO reconstruction, allowing hence the construction of non-oscillatory methods with uniform high order of accuracy in space and time.
BibTeX
@inproceedings{id602,
  address = {Delft},
  author = {E. Toro and M. Dumbser and V. Titarev and M. K{\"a}ser},
  booktitle = {Proceedings of the European Conference on Computational Fluid Dynamics, ECCOMAS},
  month = {sep},
  title = {{The Derivative Riemann Problem: The Basis for High Order ADER Schemes}},
  year = {2006},
}
EndNote
%A Toro, E.
%A Dumbser, M.
%A Titarev, V.
%A Käser, M.
%D 2006
%T The Derivative Riemann Problem: The Basis for High Order ADER Schemes
%8 sep
%C Delft
%B Proceedings of the European Conference on Computational Fluid Dynamics, ECCOMAS
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Printed 12. Dec 2019 07:14