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10964 A space-time discontinuous Galerkin finite element method for two-fluid problems

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Sollie, W.E.H. and van der Vegt, J.J.W. and Bokhove, O. (2007) A space-time discontinuous Galerkin finite element method for two-fluid problems. Memorandum 1849, Department of Applied Mathematics, University of Twente, Enschede. ISSN 1874-4850

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Abstract

A space-time discontinuous Galerkin finite element method for two fluid flow problems is presented. By using a combination of level set and cut-cell methods the interface between two fluids is tracked in space-time. The movement of the interface in space-time is calculated by solving the level set equation, where the interface geometry is identified with the 0-level set. To enhance the accuracy of the interface approximation the level set function is advected with the interface velocity, which for this purpose is extended into the domain. Close to the interface the mesh is locally refined in such a way that the 0-level set coincides with a set of faces in the mesh. The two fluid flow equations are solved on this refined mesh. The procedure is repeated until both the mesh and the flow solution have converged to a reasonable accuracy.
The method is tested on linear advection and Euler shock tube problems involving ideal gas and compressible bubbly magma. Oscillations around the interface are eliminated by choosing a suitable interface flux.

Item Type:	Internal Report (Memorandum)
Research Group:	EWI-MACS: Mathematics of Computational Science
Research Program:	IMPACT-Multiphase Fluids
Research Project:	BRICKS/MSV1: Scientific computing
Uncontrolled Keywords:	cut-cell method, discontinuous Galerkin finite element method, interface tracking, level set method, space-time, two fluid flows.
ID Code:	10964
Deposited On:	30 August 2007
International:	No
More Information:	statistics metis

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A space-time discontinuous Galerkin finite element method for two-fluid problems (deposited 30 August 2007)
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- Two fluid space-time discontinuous Galerkin finite element method. Part I: Numerical algorithm (deposited 23 November 2009)

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