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

Dumbser, Michael; Munz, Claus-Dieter

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

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AMCS, volume 17 (2007)

Abstract:

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.

Publisher:

Zielona Góra: Uniwersytet Zielonogórski

Resource Identifier:

oai:zbc.uz.zgora.pl:78654

DOI:

10.2478/v10006-007-0024-1

Pages:

297-310

Source:

AMCS, volume 17, number 3 (2007) ; click here to follow the link

Language:

eng

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Biblioteka Uniwersytetu Zielonogórskiego

Subject and keywords:

discontinuous Galerkin schemes ADER approach source terms boundary conditions unstructured meshes

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Digital Library of Zielona Góra > Repository > Faculties > Faculty of Computer, Electrical and Control Engineering

Digital Library of Zielona Góra > Repository > Types of work > Articles

Digital Library of Zielona Góra > Repository > Scientific journals and UZ publishing series > International Journal of Applied Mathematics and Computer Science (AMCS) > International Journal of Applied Mathematics and Computer Science (AMCS) (2007)

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Apr 3, 2024

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Apr 3, 2024

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https://zbc.uz.zgora.pl/publication/88409

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International Journal of Applied Mathematics and Computer Science (AMCS)

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On source terms and boundary conditions using arbitrary high order discontinuous Galerkin schemes	Apr 3, 2024

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