Pseudospectral simulation of compressible turbulence using logarithmic variables

Shebalin, John V.

doi:10.2514/6.1993-3375

Cited by 7 publications

(4 citation statements)

References 20 publications

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“…To stabilize calculations of compressible isotropic turbulence, Shebalin [38] added a bulk viscosity that was constant in space. Cook and Cabot [7,8] improved on this idea by introducing Laplacian operators that attempt to localize the artificial bulk viscosity to shocks only, and by also introducing an artificial shear viscosity (intended to mimic a subgrid model) to damp near grid-scale vortical motions:…”

Section: Appendix a Initial Conditions For The Compressible Isotropimentioning

confidence: 99%

Assessment of high-resolution methods for numerical simulations of compressible turbulence with shock waves

Johnsen

Larsson

Bhagatwala

et al. 2010

Journal of Computational Physics

350

283

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a b s t r a c tFlows in which shock waves and turbulence are present and interact dynamically occur in a wide range of applications, including inertial confinement fusion, supernovae explosion, and scramjet propulsion. Accurate simulations of such problems are challenging because of the contradictory requirements of numerical methods used to simulate turbulence, which must minimize any numerical dissipation that would otherwise overwhelm the small scales, and shock-capturing schemes, which introduce numerical dissipation to stabilize the solution. The objective of the present work is to evaluate the performance of several numerical methods capable of simultaneously handling turbulence and shock waves. A comprehensive range of high-resolution methods (WENO, hybrid WENO/central difference, artificial diffusivity, adaptive characteristic-based filter, and shock fitting) and suite of test cases (Taylor-Green vortex, Shu-Osher problem, shock-vorticity/entropy wave interaction, Noh problem, compressible isotropic turbulence) relevant to problems with shocks and turbulence are considered. The results indicate that the WENO methods provide sharp shock profiles, but overwhelm the physical dissipation. The hybrid method is minimally dissipative and leads to sharp shocks and well-resolved broadband turbulence, but relies on an appropriate shock sensor. Artificial diffusivity methods in which the artificial bulk viscosity is based on the magnitude of the strain-rate tensor resolve vortical structures well but damp dilatational modes in compressible turbulence; dilatation-based artificial bulk viscosity methods significantly improve this behavior. For well-defined shocks, the shock fitting approach yields good results.

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Section: Appendix a Initial Conditions For The Compressible Isotropimentioning

confidence: 99%

Assessment of high-resolution methods for numerical simulations of compressible turbulence with shock waves

Johnsen

Larsson

Bhagatwala

et al. 2010

Journal of Computational Physics

350

283

View full text Add to dashboard Cite

show abstract

“…One interesting approach for shock treatment was used by Shebalin [3] and then improved to an adaptive form by Cook and Cabot [4]. The key idea in these studies was to provide dissipation to the dilatational velocity field without directly affecting (dissipating) the vortical velocity field.…”

Section: Introductionmentioning

confidence: 99%

Suitability of artificial bulk viscosity for large-eddy simulation of turbulent flows with shocks

Mani

Larsson

Moin

2009

Journal of Computational Physics

108

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“…Limiters, in the form of flux limiters 4,5,23 or solution limiters, 6,22,24,25,37,40,42 are not well suited for implicit time integration schemes, and also pose challenges for high-order methods on complex geometries. As for artificial viscosity methods, Laplacian-based 15,26,28,29,35,36 and physics-based 1,9,19,20,32,35,38 approaches have been proposed. An assessment of artificial viscosity methods for unsteady flows is presented in.…”

Section: Introductionmentioning

confidence: 99%

A physics-based shock capturing method for unsteady laminar and turbulent flows

Fernández

Nguyen

Peraire

2018

2018 AIAA Aerospace Sciences Meeting

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We present a shock capturing method for unsteady laminar and turbulent flows. The proposed approach relies on physical principles to increase selected transport coefficients and resolve unstable sharp features, such as shock waves and strong thermal and shear gradients, over the smallest distance allowed by the discretization. In particular, we devise various sensors to detect when the shear viscosity, bulk viscosity and thermal conductivity of the fluid do not suffice to stabilize the numerical solution. In such cases, the transport coefficients are increased as necessary to optimally resolve these features with the available resolution. The performance of the method is illustrated through numerical simulation of external and internal flows in transonic, supersonic, and hypersonic regimes.

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Pseudospectral simulation of compressible turbulence using logarithmic variables

Cited by 7 publications

References 20 publications

Assessment of high-resolution methods for numerical simulations of compressible turbulence with shock waves

Assessment of high-resolution methods for numerical simulations of compressible turbulence with shock waves

Suitability of artificial bulk viscosity for large-eddy simulation of turbulent flows with shocks

A physics-based shock capturing method for unsteady laminar and turbulent flows

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