Volume 12, Issue 1
High Order Schemes on Three-Dimensional General Polyhedral Meshes — Application to the Level Set Method

Thibault Pringuey & R. Stewart Cant

Commun. Comput. Phys., 12 (2012), pp. 1-41.

Published online: 2012-12

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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.

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@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 = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.260511.050811a}, url = {http://global-sci.org/intro/article_detail/cicp/7282.html} }
TY - JOUR T1 - High Order Schemes on Three-Dimensional General Polyhedral Meshes — Application to the Level Set Method AU - Thibault Pringuey & R. Stewart Cant JO - Communications in Computational Physics VL - 1 SP - 1 EP - 41 PY - 2012 DA - 2012/12 SN - 12 DO - http://dor.org/10.4208/cicp.260511.050811a UR - https://global-sci.org/intro/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.

Thibault Pringuey & R. Stewart Cant. (1970). High Order Schemes on Three-Dimensional General Polyhedral Meshes — Application to the Level Set Method. Communications in Computational Physics. 12 (1). 1-41. doi:10.4208/cicp.260511.050811a
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