On high-order accurate weighted essentially non-oscillatory and discontinuous Galerkin schemes for compressible turbulence simulations

Shu, Chi‐Wang

doi:10.1098/rsta.2012.0172

Cited by 8 publications

(6 citation statements)

References 68 publications

(92 reference statements)

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“…WENO schemes and their extensions have been previously investigated in connection with different flow problems both with structured and unstructured grids, see e.g. [90,[105][106][107][108][109][110][111][112][113][114] and references therein. Note that the relative smoothness limiter of [115] is employed instead.…”

Section: Numerical Methods and Simulation Codementioning

confidence: 99%

Implicit Large Eddy Simulation of weakly-compressible turbulent channel flow

Kokkinakis¹,

Drikakis

2015

Computer Methods in Applied Mechanics and Engineering

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This paper concerns the accuracy of several high-resolution and high-order finite volume schemes in Implicit Large Eddy Simulation of weakly-compressible turbulent channel flow. The main objective is to investigate the properties of numerical schemes, originally designed for compressible flows, in low Mach compressible, near-wall turbulent flows. Variants of the Monotone Upstream-centred Scheme for Conservation Laws and Weighted Essentially Non-Oscillatory schemes for orders of accuracy ranging from second to ninth order, as well as with and without low Mach corrections, have been investigated. The performance of the schemes has been assessed against incompressible Direct Numerical Simulations. Detailed comparisons of the velocity profiles, turbulent shear stresses and higherorder turbulent statistics reveal that the low Mach correction can significantly reduce the numerical dissipation of the methods in low Mach boundary layer flows. The effects of the low Mach correction has more profound impact on second and third-order schemes, but they also improve the accuracy of fifth order schemes. The ninth-order Weighted Essentially Non-Oscillatory scheme is the least dissipative scheme and it is shown that the implementation of the low Mach correction in conjunction with this scheme has a significant anti-dissipative effect that adversely affects the accuracy. Finally, the computational cost required for obtaining the improved accuracy using increasingly higher order schemes is also discussed.

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Section: Numerical Methods and Simulation Codementioning

confidence: 99%

Implicit Large Eddy Simulation of weakly-compressible turbulent channel flow

Kokkinakis¹,

Drikakis

2015

Computer Methods in Applied Mechanics and Engineering

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“…Volume 1 consists of papers by Wang & Peters [1] on turbulence; by Klimenko [2] on thermodynamics and mixing; by Volpert et al [3] on anomalous diffusion; by Sukoriansky & Galperin [4] on analytical modelling of geophysical flows; by Bershadkii [5] on data interpretation in climate modelling; by Lozovatsky & Fernando [6] on measure for stirring efficiency in natural environments; by Majda & Gershgorin [7] on non-local diffusivity in climate variations; by Frederiksen et al [8] on stochastic modelling of geophysical flows; by Shu [9] on application of high-order accurate nonlinear schemes in simulations of compressible flows; by Radtke et al [10] on hybrid atomistic-continuum dynamic simulations of multi-scale kinetic problems; and by Sofieva et al [11] on measurements of stellar scintillations for quantification of atmospheric turbulence. These papers represent the broad variety of themes of the 'Turbulent mixing and beyond' programme [12] and are concerned with the fundamental aspects of turbulence, mixing and nonequilibrium dynamics.…”

mentioning

confidence: 99%

“…The question then is about the best alternative for handling domains with discontinuities. Shu [9] devotes his article to a review of high-order accurate weighted essentially non-oscillatory finite-difference and finitevolume schemes and the Runge-Kutta discontinuous Galerkin finite-element methods suitable for applications in compressible turbulence simulations.…”

mentioning

confidence: 99%

Turbulent mixing and beyond: non-equilibrium processes from atomistic to astrophysical scales I

Abarzhi

Gauthier²,

Sreenivasan³

2013

Phil. Trans. R. Soc. A.

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In this Introduction, we summarize and provide a perspective on 11 articles on ‘Turbulent mixing and beyond’. The papers represent the broad variety of themes of the subject, and are concerned with fundamental aspects of turbulence, mixing and non-equilibrium dynamics. While each paper deals with a specific problem, the collection gives a panoramic overview of the subject at its present state of understanding.

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“…Moreover, the upwind technique has also been used in [24][25][26] with FEM to obtain stable numerical solutions without non-physical oscillations. Furthermore, Shu et al have applied successfully the Essentially Non-Oscillatory (ENO) and Weighted Essentially NonOscillatory (WENO) schemes to obtain non-oscillatory solutions [27][28][29], in which a nonlinear adaptive procedure was used to choose local stencil automatically for higher accuracy.…”

Section: Introductionmentioning

confidence: 99%