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Solution of the generalized Riemann problem for advection-reaction equationsстатья
Статья опубликована в высокорейтинговом журнале
Статья опубликована в журнале из списка Web of Science и/или Scopus- Авторы: Toro E.F., Titarev V.A.
- Журнал: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Том: 458
- Год издания: 2002
- Издательство: Royal Society of London
- Местоположение издательства: United Kingdom
- Первая страница: 271
- Последняя страница: 271
- Аннотация: This paper concerns the construction of non-oscillatory schemes of very highorder of accuracy in space and time, to solve non-linear hyperbolic conservationlaws. The schemes result from extending the ADER approach, which is relatedto the ENO/WENO methodology. Our schemes are conservative, one-step,explicit and fully discrete, requiring only the computation of the inter-cell fluxesto advance the solution by a full time step; the schemes have optimal stabilitycondition. To compute the intercell flux in one space dimension we solve ageneralised Riemann problem by reducing it to the solution a sequence of mconventional Riemann problems for the kth spatial derivatives of the solution,with k=0, 1,..., m − 1, where m is arbitrary and is the order of the accuracy ofthe resulting scheme. We provide numerical examples using schemes of up tofifth order of accuracy in both time and space.
- Добавил в систему: Титарев Владимир Александрович