Embedded turbulence model in numerical methods for hyperbolic conservation laws

Drikakis, Dimitris

doi:10.1002/fld.328

Cited by 38 publications

(16 citation statements)

References 35 publications

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“…The present simulations can thus be interpreted as a class of implicit large-eddy simulations (ILES) [2,[8][9][10], in which the equations are implicitly filtered by the discretization and the numerical dissipation is a surrogate for an explicit subgrid-scale model. As the nondissipative compressible fluid dynamics equations are formally ill-posed, this numerical dissipation regularizes the numerical method.…”

Section: Equations Solved and Description Of The Weno Algorithmmentioning

confidence: 99%

High-order WENO simulations of three-dimensional reshocked Richtmyer–Meshkov instability to late times: dynamics, dependence on initial conditions, and comparisons to experimental data

Schilling

Latini

2010

Acta Mathematica Scientia

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The dynamics of the reshocked multi-mode Richtmyer-Meshkov instability is investigated using 513 × 257 2 three-dimensional ninth-order weighted essentially nonoscillatory shock-capturing simulations. A two-mode initial perturbation with superposed random noise is used to model the Mach 1.5 air/SF 6 Vetter-Sturtevant shock tube experiment. The mass fraction and enstrophy isosurfaces, and density cross-sections are utilized to show the detailed flow structure before, during, and after reshock. It is shown that the mixing layer growth agrees well with the experimentally measured growth rate before and after reshock. The post-reshock growth rate is also in good agreement with the prediction of the Mikaelian model. A parametric study of the sensitivity of the layer growth to the choice of amplitudes of the short and long wavelength initial interfacial perturbation is also presented. Finally, the amplification effects of reshock are quantified using the evolution of the turbulent kinetic energy and turbulent enstrophy spectra, as well as the evolution of the baroclinic enstrophy production, buoyancy production, and shear production terms in the enstrophy and turbulent kinetic transport equations.

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Section: Equations Solved and Description Of The Weno Algorithmmentioning

confidence: 99%

High-order WENO simulations of three-dimensional reshocked Richtmyer–Meshkov instability to late times: dynamics, dependence on initial conditions, and comparisons to experimental data

Schilling

Latini

2010

Acta Mathematica Scientia

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“…The present simulations can be interpreted as a class of implicit large-eddy simulations (ILES) [15][16][17][18], in which the equations are implicitly filtered by the discretization and the numerical dissipation is a surrogate for a dissipation provided by an explicit subgrid-scale model. As the non-dissipative compressible fluid dynamics equations are formally ill-posed, this numerical dissipation regularizes the method.…”

Section: Equations Solved and Description Of The Weno Algorithmmentioning

confidence: 99%

Effects of WENO flux reconstruction order and spatial resolution on reshocked two-dimensional Richtmyer-Meshkov instability

Latini

Schilling

Don

2006

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Weighted essentially non-oscillatory (WENO) simulations of the reshocked twodimensional single-mode Richtmyer-Meshkov instability using third-, fifth-and ninthorder spatial flux reconstruction and uniform grid resolutions corresponding to 128, 256 and 512 points per initial perturbation wavelength are presented. The dependence of the density, vorticity, simulated density Schlieren and baroclinic production fields, mixing layer width, circulation deposition, mixing profiles, production and mixing fractions, energy spectra, statistics, probability distribution functions, numerical turbulent kinetic energy and enstrophy production/dissipation rates, numerical Reynolds numbers, and numerical viscosity on the order and resolution is investigated to long evolution times. The results are interpreted using the implicit numerical dissipation in the characteristic projection-based, finite-difference WENO method. It is shown that higher order higher resolution simulations have lower numerical dissipation. The sensitivity of the quantities considered to the order and resolution is further amplified following reshock, when the energy deposition by the second shock-interface interaction induces the formation of small-scale structures. Lower-order lower-resolution simulations preserve large-scale structures and flow symmetry to late times, while higher-order higher-resolution simulations exhibit fragmentation of the structures, symmetry breaking and increased mixing. Similar flow features are qualitatively and quantitatively captured by either approximately doubling the order or the resolution. Additionally, the computational scaling shows that increasing the order is more advantageous than increasing the resolution for the flow considered here. The present investigation suggests that the ninth-order WENO method is well-suited for the simulation and analysis of complex multi-scale flows and mixing generated by shock-induced hydrodynamic instabilities.

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“…2). This problem has been extensively studied for single fluid cases, including linear stability analysis [36], and has become an established test bed for comparison of different numerical schemes [37][38][39][40][41]. A temporal (reacting) shear layer and the effect of non-uniform density on its development have been studied by Ghoniem et al [43,44].…”

Section: Introductionmentioning

confidence: 99%

Artificial compressibility, characteristics-based schemes for variable-density, incompressible, multispecies flows: Part II. Multigrid implementation and numerical tests

Shapiro

Drikakis

2005

Journal of Computational Physics

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The paper presents an investigation of the accuracy and efficiency of artificial compressibility, characteristics-based (CB) schemes for variable-density incompressible flows. The CB schemes have been implemented in conjunction with a multigrid method for accelerating numerical convergence and a fourth-order, explicit Runge-Kutta method for the integration of the governing equations in time. The implementation of the CB schemes is obtained in conjunction with first-, second-and third-order interpolation formulas for calculating the variables at the cell faces of the computational volume. The accuracy and efficiency of the schemes are examined against analytical and experimental results for diffusion broadening in two-and three-dimensional microfluidic channels, a problem that has motivated the development of the present methods. Moreover, unsteady, inviscid simulations have been performed for variable-density mixing layer. The computations revealed that accuracy and efficiency depend on the CB scheme design. The best multigrid convergence rates were exhibited by the conservative CB scheme, which is obtained by the fully conservative formulation of the variable-density, incompressible equations.

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Embedded turbulence model in numerical methods for hyperbolic conservation laws

Cited by 38 publications

References 35 publications

High-order WENO simulations of three-dimensional reshocked Richtmyer–Meshkov instability to late times: dynamics, dependence on initial conditions, and comparisons to experimental data

High-order WENO simulations of three-dimensional reshocked Richtmyer–Meshkov instability to late times: dynamics, dependence on initial conditions, and comparisons to experimental data

Effects of WENO flux reconstruction order and spatial resolution on reshocked two-dimensional Richtmyer-Meshkov instability

Artificial compressibility, characteristics-based schemes for variable-density, incompressible, multispecies flows: Part II. Multigrid implementation and numerical tests

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