Universität zu Köln

Gassner, Gregor, Staudenmaier, Marc, Hindenlang, Florian, Atak, Muhammed and Munz, Claus-Dieter (2015). A space-time adaptive discontinuous Galerkin scheme. Comput. Fluids, 117. S. 247 - 262. OXFORD: PERGAMON-ELSEVIER SCIENCE LTD. ISSN 1879-0747

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Abstract

A discontinuous Galerkin scheme for unsteady fluid flows is described that allows a very high level of adaptive control in the space-time domain. The scheme is based on an explicit space-time predictor, which operates locally and takes the time evolution of the data within the grid cell into account. The predictor establishes a local space-time approximate solution in a whole space-time grid cell. This enables a time-consistent local time-stepping, by which the approximate solution is advanced in time in every grid cell with its own time step, only restricted by the local explicit stability condition. The coupling of the grid cells is solely accomplished by the corrector which is determined by the numerical fluxes. The considered discontinuous Galerldn scheme allows non-conforming meshes, together with p-adaptivity in 3 dimensions and h/p-adaptivity in 2 dimensions. Hence, we combine in this scheme all the flexibility that the discontinuous Galerkin approach provides. In this work, we investigate the combination of the local time-stepping with h- and p-adaptivity. Complex unsteady flow problems are presented to demonstrate the advantages of such an adaptive framework for simulations with strongly varying resolution requirements, e.g. shock waves, boundary layers or turbulence. (C) 2015 Elsevier Ltd. All rights reserved.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Gassner, Gregor UNSPECIFIED UNSPECIFIED UNSPECIFIED Staudenmaier, Marc UNSPECIFIED UNSPECIFIED UNSPECIFIED Hindenlang, Florian UNSPECIFIED UNSPECIFIED UNSPECIFIED Atak, Muhammed UNSPECIFIED UNSPECIFIED UNSPECIFIED Munz, Claus-Dieter UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-396124
DOI:	10.1016/j.compfluid.2015.05.002
Journal or Publication Title:	Comput. Fluids
Volume:	117
Page Range:	S. 247 - 262
Date:	2015
Publisher:	PERGAMON-ELSEVIER SCIENCE LTD
Place of Publication:	OXFORD
ISSN:	1879-0747
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language NAVIER-STOKES EQUATIONS; FINITE-ELEMENT-METHOD; COMPRESSIBLE EULER EQUATIONS; HYPERBOLIC CONSERVATION-LAWS; DYNAMIC GRID MOTION; RUNGE-KUTTA METHODS; UNSTRUCTURED MESHES; ELLIPTIC PROBLEMS; FLOW; FORMULATION Multiple languages Computer Science, Interdisciplinary Applications; Mechanics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/39612