High-order gas-kinetic scheme on three-dimensional unstructured meshes for compressible flows

2021 ◽  
Vol 33 (9) ◽  
pp. 096102
Author(s):  
Yaqing Yang ◽  
Liang Pan ◽  
Kun Xu
Keyword(s):  
Compressible Flows ◽  
Three Dimensional ◽  
Kinetic Scheme ◽  
Unstructured Meshes ◽  
High Order

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

2012 ◽  
Vol 12 (1) ◽  
pp. 1-41 ◽  
Author(s):  
Thibault Pringuey ◽  
R. Stewart Cant
Keyword(s):  
Level Set ◽  
Three Dimensional ◽  
Unstructured Meshes ◽  
High Order ◽  
Convex Polyhedra ◽  
Two Phase ◽  
High Order Schemes ◽  
Flow Problems ◽  
Mixed Element ◽  
Areas Of Interest

AbstractIn 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.

A High-Order Central ENO Finite-Volume Scheme for Three-Dimensional Low-Speed Viscous Flows on Unstructured Mesh

2015 ◽  
Vol 17 (3) ◽  
pp. 615-656 ◽  
Author(s):  
Marc R. J. Charest ◽  
Clinton P. T. Groth ◽  
Pierre Q. Gauthier
Keyword(s):  
Finite Volume ◽  
Unstructured Mesh ◽  
Incompressible Flows ◽  
Three Dimensional ◽  
Viscous Flows ◽  
Unstructured Meshes ◽  
High Order ◽  
Finite Volume Scheme ◽  
Low Speed ◽  
Volume Scheme

AbstractHigh-order discretization techniques offer the potential to significantly reduce the computational costs necessary to obtain accurate predictions when compared to lower-order methods. However, efficient and universally-applicable high-order discretizations remain somewhat illusive, especially for more arbitrary unstructured meshes and for incompressible/low-speed flows. A novel, high-order, central essentially non-oscillatory (CENO), cell-centered, finite-volume scheme is proposed for the solution of the conservation equations of viscous, incompressible flows on three-dimensional unstructured meshes. Similar to finite element methods, coordinate transformations are used to maintain the scheme’s order of accuracy even when dealing with arbitrarily-shaped cells having non-planar faces. The proposed scheme is applied to the pseudo-compressibility formulation of the steady and unsteady Navier-Stokes equations and the resulting discretized equations are solved with a parallel implicit Newton-Krylov algorithm. For unsteady flows, a dual-time stepping approach is adopted and the resulting temporal derivatives are discretized using the family of high-order backward difference formulas (BDF). The proposed finite-volume scheme for fully unstructured mesh is demonstrated to provide both fast and accurate solutions for steady and unsteady viscous flows.

scholarly journals A high-order vertex-based central ENO finite-volume scheme for three-dimensional compressible flows

2015 ◽  
Vol 114 ◽  
pp. 172-192 ◽  
Author(s):  
Marc R.J. Charest ◽  
Thomas R. Canfield ◽  
Nathaniel R. Morgan ◽  
Jacob Waltz ◽  
John G. Wohlbier
Keyword(s):  
Finite Volume ◽  
Compressible Flows ◽  
Three Dimensional ◽  
High Order ◽  
Finite Volume Scheme ◽  
Volume Scheme
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