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A high-order low-dispersion symmetry-preserving finite-volume method for compressible flow on curvilinear grids

Published: 01 October 2009 Publication History

Abstract

A new high-order finite-volume method is presented that preserves the skew symmetry of convection for the compressible flow equations. The method is intended for Large-Eddy Simulations (LES) of compressible turbulent flows, in particular in the context of hybrid RANS-LES computations. The method is fourth-order accurate and has low numerical dissipation and dispersion. Due to the finite-volume approach, mass, momentum, and total energy are locally conserved. Furthermore, the skew-symmetry preservation implies that kinetic energy, sound-velocity, and internal energy are all locally conserved by convection as well. The method is unique in that all these properties hold on non-uniform, curvilinear, structured grids. Due to the conservation of kinetic energy, there is no spurious production or dissipation of kinetic energy stemming from the discretization of convection. This enhances the numerical stability and reduces the possible interference of numerical errors with the subgrid-scale model. By minimizing the numerical dispersion, the numerical errors are reduced by an order of magnitude compared to a standard fourth-order finite-volume method.

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  1. A high-order low-dispersion symmetry-preserving finite-volume method for compressible flow on curvilinear grids

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        Published In

        cover image Journal of Computational Physics
        Journal of Computational Physics  Volume 228, Issue 18
        October, 2009
        512 pages

        Publisher

        Academic Press Professional, Inc.

        United States

        Publication History

        Published: 01 October 2009

        Author Tags

        1. 65M06
        2. 76F65
        3. 76M12
        4. Compressible flow
        5. Conservation properties
        6. Curvilinear grids
        7. Finite-volume
        8. High-order discretization
        9. Large-Eddy Simulation
        10. Low dispersion
        11. Skew-symmetric form

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        • (2015)Energy preserving turbulent simulations at a reduced computational costJournal of Computational Physics10.1016/j.jcp.2015.06.011298:C(480-494)Online publication date: 1-Oct-2015
        • (2014)Isotropic finite volume discretizationJournal of Computational Physics10.1016/j.jcp.2014.07.025276:C(252-290)Online publication date: 1-Nov-2014
        • (2013)An energy preserving formulation for the simulation of multiphase turbulent flowsJournal of Computational Physics10.5555/2743140.2743565235:C(114-128)Online publication date: 15-Feb-2013
        • (2012)Mass, momentum and energy conserving (MaMEC) discretizations on general grids for the compressible Euler and shallow water equationsJournal of Computational Physics10.1016/j.jcp.2012.03.005231:14(4723-4744)Online publication date: 1-May-2012
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