TY - JOUR T1 - High Order Schemes on Three-Dimensional General Polyhedral Meshes — Application to the Level Set Method JO - Communications in Computational Physics VL - 1 SP - 1 EP - 41 PY - 2012 DA - 2012/12 SN - 12 DO - http://doi.org/10.4208/cicp.260511.050811a UR - https://global-sci.org/intro/article_detail/cicp/7282.html KW - AB -

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.