Using Fourth Order Accurate Spatial Integration on Unstructured Meshes to Reduce LES Run Times

Khosla, Sachin; Dionne, Paul J.; Lee, Michael E.; Smith, Clifford E.; Sekar, Balu; Afb, Wright-Patterson

doi:10.2514/6.2008-782

Cited by 4 publications

(3 citation statements)

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“…The growing need for industrial applications of Large Eddy Simulations on unstructured grids makes this question more stringent than before. This topic is still an active field of research [2,11,16,31,35,36,51].…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of the cell centered finite-volume Muscl method on unstructured grids

2009

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The goal of this study is to apply the Muscl scheme to the linear advection equation on general unstructured grids and to examine the eigenvalue stability of the resulting linear semi-discrete equation. Although this semi-discrete scheme is in general stable on cartesian grids, numerical calculations of spectra show that this can sometimes fail for generalizations of the Muscl method to unstructured three-dimensional grids. This motivates our investigation of the influence of the slope reconstruction method and stencil on the eigenvalue stability of the Muscl scheme. A theoretical stability analysis of the first order upwind scheme proves that this method is stable on arbitrary grids. In contrast, a general theoretical result is very difficult to obtain for the Muscl scheme. We are able to identify a local property of the slope reconstruction that is strongly related to the appearance of unstable eigenmodes. This property allows to identify the reconstruction methods that are best suited for stable discretizations. The explicit numerical computation of spectra for a large number of two-and three-dimensional test cases confirms and completes the theoretical results.Keywords Finite volume scheme · Stability analysis · Hyperbolic equations · Dynamical systems · Method of lines · Muscl method F. Haider (B) · B. Courbet Département de simulation numérique des écoulements et aéroacoustique, ONERA,

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Section: Introductionmentioning

confidence: 99%

Stability analysis of the cell centered finite-volume Muscl method on unstructured grids

2009

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“…Another option [9] is where the reconstruction in finite volumes is considered in the general framework of the Discontinuous Galerkin approach. We also refer to the studies [19,31], with interest into application oriented simulations, where reconstructions beyond linear are presented. Finally we mention the recent study [23] where a variant of compact k-exact reconstruction is considered.…”

Section: Related Workmentioning

confidence: 99%

A high-order interpolation for the finite volume method: The Coupled Least Squares reconstruction

2018

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We consider the Finite Volume Method on irregular grids for conservation laws with a particular polynomial reconstruction. This reconstruction is based on a least squares approach to compute consistent approximations of the first, second and third order derivatives. The resulting reconstruction is cubic. It is called the Coupled Least Squares reconstruction. It is obtained by a three stages iteration. At each iteration, only data located in a compact stencil, and not beyond, are accessed. A linear stability analysis is given in the case of regular and irregular one-dimensional grids. Numerical results for various problems, including shock tubes, vortex and accoustic wave propagation, support the interest of this approach. The reconstruction algorithm is presented in detail in the one dimensional case. An outline of the multidimensional case in also given. This work was announced in [14].

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“…The quadratic approach was extended to unstructured grids [1,2]. The need for large (non compact) stencils seems to have limited the use of cubic reconstructions (4 th order), although some practical applications exist [5].…”

Section: Introductionmentioning

confidence: 99%

Efficient Implementation of High Order Reconstruction in Finite Volume Methods

Haider

Brenner²,

Courbet

et al. 2011

Finite Volumes for Complex Applications VI Problems &Amp; Perspectives

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Using Fourth Order Accurate Spatial Integration on Unstructured Meshes to Reduce LES Run Times

Cited by 4 publications

References 1 publication

Stability analysis of the cell centered finite-volume Muscl method on unstructured grids

Stability analysis of the cell centered finite-volume Muscl method on unstructured grids

A high-order interpolation for the finite volume method: The Coupled Least Squares reconstruction

Efficient Implementation of High Order Reconstruction in Finite Volume Methods

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