scholarly journals Construction of very high order residual distribution schemes for steady inviscid flow problems on hybrid unstructured meshes

2011 ◽  
Vol 230 (11) ◽  
pp. 4103-4136 ◽  
Author(s):  
R. Abgrall ◽  
A. Larat ◽  
M. Ricchiuto
Keyword(s):  
Inviscid Flow ◽  
Unstructured Meshes ◽  
High Order ◽  
Residual Distribution ◽  
Flow Problems ◽  
Residual Distribution Schemes ◽  
Very High

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 simple construction of very high order non-oscillatory compact schemes on unstructured meshes

2009 ◽  
Vol 38 (7) ◽  
pp. 1314-1323 ◽  
Author(s):  
R. Abgrall ◽  
A. Larat ◽  
M. Ricchiuto ◽  
C. Tavé
Keyword(s):  
Unstructured Meshes ◽  
High Order ◽  
Compact Schemes ◽  
Simple Construction ◽  
Very High

High-order upwind residual distribution schemes on isoparametric curved elements

2011 ◽  
Vol 230 (4) ◽  
pp. 890-906 ◽  
Author(s):  
Martin Vymazal ◽  
Tiago Quintino ◽  
Nadège Villedieu ◽  
Herman Deconinck
Keyword(s):  
High Order ◽  
Residual Distribution ◽  
Residual Distribution Schemes ◽  
Curved Elements

The Simulation of the Linearized Euler Equations by a Second Order Scheme is Possible

2005 ◽  
Vol 4 (1-2) ◽  
pp. 49-68
Author(s):  
R. Abgrall ◽  
M. Ravachol ◽  
S. Marret
Keyword(s):  
Numerical Simulation ◽  
Euler Equations ◽  
Finite Volume ◽  
Unstructured Meshes ◽  
High Order ◽  
Complex Geometries ◽  
Residual Distribution ◽  
Linearized Euler Equations ◽  
Order Scheme ◽  
The One

We are interested in the numerical simulation of acoustic perturbations via the linearized Euler equations using triangle unstructured meshes in complex geometries such as the one around a complete aircraft. It is known that the classical schemes using a finite volume formulation with high order extrapolation of the variables can be very disappointing. In this paper, we show that using an upwind residual distribution formulation, it is possible to simulate such problems, even on truly unstructured meshes. The main focus of the paper is on the propagative properties of the scheme.

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