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High Order Schemes on Three-Dimensional General Polyhedral Meshes — Application to the Level Set Method

Published online by Cambridge University Press:  20 August 2015

Thibault Pringuey  and
R. Stewart Cant
Thibault Pringuey*
Affiliation:
CFD Laboratory, Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
R. Stewart Cant*
Affiliation:
CFD Laboratory, Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
*
Corresponding author.Email:tp299@cam.ac.uk
Email:rsc10@cam.ac.uk
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Abstract

In this article, we detail the methodology developed to construct arbitrarily high order schemes — linear and WENO — on 3D mixed-element unstructured meshes made up of general convex polyhedral elements. The approach is tailored specifically for the solution of scalar level set equations for application to incompressible two-phase flow problems. The construction of WENO schemes on 3D unstructured meshes is notoriously difficult, as it involves a much higher level of complexity than 2D approaches. This due to the multiplicity of geometrical considerations introduced by the extra dimension, especially on mixed-element meshes. Therefore, we have specifically developed a number of algorithms to handle mixed-element meshes composed of convex polyhedra with convex polygonal faces. The contribution of this work concerns several areas of interest: the formulation of an improved methodology in 3D, the minimisation of computational runtime in the implementation through the maximum use of pre-processing operations, the generation of novel methods to handle complex 3D mixed-element meshes and finally the application of the method to the transport of a scalar level set.

Keywords

65M0876-0476N99WENO schemethree-dimensionalunstructured meshmixed elementpolyhedral elementhyperbolic equationslevel set
Type
Research Article
Information
Communications in Computational Physics , Volume 12 , Issue 1 , July 2012 , pp. 1 - 41
Copyright
Copyright © Global Science Press Limited 2012

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