Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 228, Issue 21, Pages 8161-8186Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2009.07.036
Keywords
High-order methods; Euler equations; Unstructured grids; Discontinuous Galerkin; Spectral volume; Spectral difference; Collocation; Finite difference
Funding
- AFOSR [FA9550-06-1-0146]
- DOE [DE- FG02- 05ER25677]
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Recently a new high-order formulation for 1D conservation laws was developed by Huynh using the idea of flux reconstruction. The formulation was capable of unifying several popular methods including the discontinuous Galerkin, staggered-grid multi-domain method, or the spectral difference/spectral volume methods into a single family. The extension of the method to quadrilateral and hexahedral elements is straightforward. In an attempt to extend the method to other element types such as triangular, tetrahedral or prismatic elements, the idea of flux reconstruction is generalized into a lifting collocation penalty approach. With a judicious selection of solution points and flux points, the approach can be made simple and efficient to implement for mixed grids. In addition, the formulation includes the discontinuous Galerkin, spectral volume and spectral difference methods as special cases. Several test problems are presented to demonstrate the capability of the method. (C) 2009 Elsevier Inc. All rights reserved.
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