2013
DOI: 10.1098/rsta.2012.0172
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On high-order accurate weighted essentially non-oscillatory and discontinuous Galerkin schemes for compressible turbulence simulations

Abstract: One contribution of 13 to a Theme Issue 'Turbulent mixing and beyond: non-equilibrium processes from atomistic to astrophysical scales I' . In this article, we give a brief overview on high-order accurate shock capturing schemes with the aim of applications in compressible turbulence simulations. The emphasis is on the basic methodology and recent algorithm developments for two classes of high-order methods: the weighted essentially non-oscillatory and discontinuous Galerkin methods.

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Cited by 8 publications
(6 citation statements)
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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%
“…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%
“…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%
“…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%