Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 258, Issue -, Pages 246-267Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2013.10.031
Keywords
Symmetry preserving discretization; Collocated formulation; Unstructured grid; Checkerboard; Regularization; Differentially heated cavity
Funding
- Ministerio de Ciencia e Innovacion, Spain [ENE2010-17801]
- Generalitat de Catalunya Beatriu de Pinos postdoctoral fellowship [2006 BP-A 10075]
- Juan de la Cierva postdoctoral contract by the Ministerio de Ciencia e Innovacion [JCI-2009-04910]
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A fully-conservative discretization is presented in this paper. The same principles followed by Verstappen and Veldman (2003) [3] are generalized for unstructured meshes. Here, a collocated-mesh scheme is preferred over a staggered one due to its simpler form for such meshes. The basic idea behind this approach remains the same: mimicking the crucial symmetry properties of the underlying differential operators, i.e., the convective operator is approximated by a skew-symmetric matrix and the diffusive operator by a symmetric, positive-definite matrix. A novel approach to eliminate the checkerboard spurious modes without introducing any non-physical dissipation is proposed. To do so, a fully-conservative regularization of the convective term is used. The supraconvergence of the method is numerically showed and the treatment of boundary conditions is discussed. Finally, the new discretization method is successfully tested for a buoyancy-driven turbulent flow in a differentially heated cavity. (C) 2013 Elsevier Inc. All rights reserved.
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