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2007 | 17 | 3 | 297-310
Tytuł artykułu

On source terms and boundary conditions using arbitrary high order discontinuous Galerkin schemes

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This article is devoted to the discretization of source terms and boundary conditions using discontinuous Galerkin schemes with an arbitrary high order of accuracy in space and time for the solution of hyperbolic conservation laws on unstructured triangular meshes. The building block of the method is a particular numerical flux function at the element interfaces based on the solution of Generalized Riemann Problems (GRPs) with piecewise polynomial initial data. The solution of the generalized Riemann problem, originally introduced by Toro and Titarev in a finite volume context, provides simultaneously a numerical flux function as well as a time integration method. The resulting scheme is extremely local since it integrates the PDE from one time step to the successive one in a single step using only information from the direct side neighbors. Since source terms are directly incorporated into the numerical flux via the solution of the GRP, our very high order accurate method is also able to maintain very well smooth steady-state solutions of PDEs with source terms, similar to the so-called well-balanced schemes which are usually specially designed for this purpose. Boundary conditions are imposed solving inverse generalized Riemann problems. Furthermore, we show numerical evidence proving that by using very high order schemes together with high order polynomial representations of curved boundaries, high quality solutions can be obtained on very coarse meshes.
Rocznik
Tom
17
Numer
3
Strony
297-310
Opis fizyczny
Daty
wydano
2007
poprawiono
2006-05-10
(nieznana)
2006-12-15
Twórcy
  • Institut für Aerodynamik und Gasdynamik, Pfaffenwaldring 21, D-70550 Stuttgart, Germany
  • Institut für Aerodynamik und Gasdynamik, Pfaffenwaldring 21, D-70550 Stuttgart, Germany
Bibliografia
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  • Dumbser M. (2005): Arbitrary High Order Schemes for the Solution of Hyperbolic Conservation Laws in Complex Domains. Aachen: Shaker Verlag.
  • Dumbser M. and Munz C.D. (2005): Arbitrary high order Discontinuous Galerkin schemes, In: Numerical Methods for Hyperbolic and Kinetic Problems (S. Cordier, T. Goudon, M. Gutnicand E. Sonnendrucker, Eds.). EMS Publishing House, pp.295-333.
  • Dumbser M. and Munz C.D. (2006): Building blocks for arbitrary high order discontinuous Galerkin schemes. Journal of Scientific Computing, Vol.27, pp.215-230.
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  • Press W.H., Teukolsky S.A., Vetterling W.T. and Flannery B.P. (1996): Numerical Recipes in Fortran 77. Cambridge: Cambridge University Press.
  • Qiu J., Dumbser M. and Shu C.W. (2005): The discontinuous Galerkin method with Lax-Wendroff type time discretizations. Computer Methods in Applied Mechanics and Engineering, Vol.194, pp.4528-4543.
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  • Toro E.F. (1999): Riemann Solvers and Numerical Methods for Fluid Dynamics, 2nd Ed. Springer.
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Typ dokumentu
Bibliografia
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