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research-article

Reduced aliasing formulations of the convective terms within the Navier-Stokes equations for a compressible fluid

Authors:

Christopher A. Kennedy,

Andrea GruberAuthors Info & Claims

Journal of Computational Physics, Volume 227, Issue 3

Pages 1676 - 1700

https://doi.org/10.1016/j.jcp.2007.09.020

Published: 01 January 2008 Publication History

Abstract

The effect on aliasing errors of different formulations describing the cubically nonlinear convective terms within the discretized Navier-Stokes equations is examined in the presence of a non-trivial density spectrum. Fourier analysis shows that the existing skew-symmetric forms of the convective term result in reduced aliasing errors relative to the conservation form. Several formulations of the convective term, including a new formulation proposed for cubically nonlinear terms, are tested in direct numerical simulation (DNS) of decaying compressible isotropic turbulence both in chemically inert (small density fluctuations) and reactive cases (large density fluctuations) and for different degrees of resolution. In the DNS of reactive turbulent flow, the new cubic skew-symmetric form gives the most accurate results, consistent with the spectral error analysis, and at the lowest cost. In marginally resolved DNS and LES (poorly resolved by definition) the new cubic skew-symmetric form represents a robust convective formulation which minimizes both aliasing and computational cost while also allowing a reduction in the use of computationally expensive high-order dissipative filters.

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Cited By

Yee HSjögreen B(2023)Recent advancement of entropy split methods for compressible gas dynamics and MHDApplied Mathematics and Computation10.1016/j.amc.2022.127545439:COnline publication date: 15-Feb-2023
https://dl.acm.org/doi/10.1016/j.amc.2022.127545
Gassner GSvärd MHindenlang F(2022)Stability Issues of Entropy-Stable and/or Split-form High-order SchemesJournal of Scientific Computing10.1007/s10915-021-01720-890:3Online publication date: 1-Mar-2022
https://dl.acm.org/doi/10.1007/s10915-021-01720-8
Sjögreen BYee HKotov DKritsuk A(2020)Skew-Symmetric Splitting for Multiscale Gas Dynamics and MHD Turbulence FlowsJournal of Scientific Computing10.1007/s10915-020-01225-w83:3Online publication date: 22-May-2020
https://dl.acm.org/doi/10.1007/s10915-020-01225-w
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Index Terms

Reduced aliasing formulations of the convective terms within the Navier-Stokes equations for a compressible fluid
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Partial differential equations
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Error-correcting codes

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Published In

cover image Journal of Computational Physics

Journal of Computational Physics Volume 227, Issue 3

January, 2008

578 pages

ISSN:0021-9991

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Copyright © Elsevier Inc.

Publisher

Academic Press Professional, Inc.

United States

Publication History

Published: 01 January 2008

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Cited By

Yee HSjögreen B(2023)Recent advancement of entropy split methods for compressible gas dynamics and MHDApplied Mathematics and Computation10.1016/j.amc.2022.127545439:COnline publication date: 15-Feb-2023
https://dl.acm.org/doi/10.1016/j.amc.2022.127545
Gassner GSvärd MHindenlang F(2022)Stability Issues of Entropy-Stable and/or Split-form High-order SchemesJournal of Scientific Computing10.1007/s10915-021-01720-890:3Online publication date: 1-Mar-2022
https://dl.acm.org/doi/10.1007/s10915-021-01720-8
Sjögreen BYee HKotov DKritsuk A(2020)Skew-Symmetric Splitting for Multiscale Gas Dynamics and MHD Turbulence FlowsJournal of Scientific Computing10.1007/s10915-020-01225-w83:3Online publication date: 22-May-2020
https://dl.acm.org/doi/10.1007/s10915-020-01225-w
Ranocha H(2018)Comparison of Some Entropy Conservative Numerical Fluxes for the Euler EquationsJournal of Scientific Computing10.1007/s10915-017-0618-176:1(216-242)Online publication date: 1-Jul-2018
https://dl.acm.org/doi/10.1007/s10915-017-0618-1
Modesti DPirozzoli S(2018)An Efficient Semi-implicit Solver for Direct Numerical Simulation of Compressible Flows at All SpeedsJournal of Scientific Computing10.1007/s10915-017-0534-475:1(308-331)Online publication date: 1-Apr-2018
https://dl.acm.org/doi/10.1007/s10915-017-0534-4
Wintermeyer NWinters AGassner GKopriva D(2017)An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetryJournal of Computational Physics10.1016/j.jcp.2017.03.036340:C(200-242)Online publication date: 1-Jul-2017
https://dl.acm.org/doi/10.1016/j.jcp.2017.03.036
Schlanderer SWeymouth GSandberg R(2017)The boundary data immersion method for compressible flows with application to aeroacousticsJournal of Computational Physics10.1016/j.jcp.2016.12.050333:C(440-461)Online publication date: 15-Mar-2017
https://dl.acm.org/doi/10.1016/j.jcp.2016.12.050
Gassner GWinters AKopriva D(2016)Split form nodal discontinuous Galerkin schemes with summation-by-parts property for the compressible Euler equationsJournal of Computational Physics10.1016/j.jcp.2016.09.013327:C(39-66)Online publication date: 15-Dec-2016
https://dl.acm.org/doi/10.1016/j.jcp.2016.09.013
Yu CBhumkar YSheu T(2015)Dispersion Relation Preserving Combined Compact Difference Schemes for Flow ProblemsJournal of Scientific Computing10.1007/s10915-014-9864-762:2(482-516)Online publication date: 1-Feb-2015
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Salvadore FBernardini MBotti M(2013)GPU accelerated flow solver for direct numerical simulation of turbulent flowsJournal of Computational Physics10.5555/2743140.2743566235:C(129-142)Online publication date: 15-Feb-2013
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