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High order schemes on three-dimensional general polyhedral meshes - Application to the level set method

Pringuey, T and Cant, RS (2012) High order schemes on three-dimensional general polyhedral meshes - Application to the level set method. Communications in Computational Physics, 12. pp. 1-41. ISSN 1815-2406

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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. © 2012 Global-Science Press.

Item Type: Article
Uncontrolled Keywords: Hyperbolic equations Level set Mixed element Polyhedral element Three-dimensional Unstructured mesh WENO scheme
Divisions: Div A > Energy
Depositing User: Unnamed user with email
Date Deposited: 16 Jul 2015 13:48
Last Modified: 28 Aug 2015 23:17
DOI: 10.4208/cicp.260511.050811a