@Article{CiCP-12-1,
author = {Thibault Pringuey and R. Stewart Cant},
title = {High Order Schemes on Three-Dimensional General Polyhedral Meshes — Application to the Level Set Method},
journal = {Communications in Computational Physics},
year = {2012},
volume = {12},
number = {1},
pages = {1--41},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.260511.050811a},
url = {http://global-sci.org/intro/article_detail/cicp/7282.html}
}