Large eddy simulation requirements for the Richtmyer-Meshkov instability

Olson, Britton J.; Greenough, Jeffrey A.

doi:10.1063/1.4871396

Cited by 44 publications

(22 citation statements)

References 33 publications

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“…The results suggest that although the time window of simulations has been extended thanks to the hybrid method, the flow has not yet become fully self-similar. Olson and Greenough (2014) suggested that the required number of grid points needed for a DNS of RMI is about 4 × 10 12 , which exceeds the current capabilities of super-computing resources. For an RM calculation with fixed small scales computed with an explicit hydrodynamics scheme, the computational cost to get to width W will be ∝ W 3 W 1/θ , where the first term is the number of cells required to resolve the mixing layer and the second term is the number of timesteps required.…”

Section: Discussionmentioning

confidence: 99%

Computing multi-mode shock-induced compressible turbulent mixing at late times

et al. 2015

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Both experiments and numerical simulations pertinent to the study of self-similarity in shock-induced turbulent mixing often do not cover sufficiently long enough times for the mixing layer to become developed in a fully turbulent manner. When the Mach number of the flow is sufficiently low, numerical simulations based on the compressible flow equations tend to become less accurate due to inherent numerical cancellation errors. This paper concerns a numerical study of the late time behaviour of single-shocked Richtmyer-Meshkov Instability (RMI) and associated compressible turbulent mixing using a new technique that addresses the above limitation. The present approach exploits the fact that RMI is a compressible flow during the early stages of the simulation and incompressible at late times. Therefore, depending on the compressibility of the flow field the most suitable model, compressible or incompressible, can be employed. This motivates the development of a hybrid compressible-incompressible solver that removes the low-Mach number limitations of the compressible solvers, thus allowing numerical simulations of late time mixing. Simulations have been performed for a multi-mode perturbation at the interface between two fluids of densities corresponding to an Atwood number of 0.5, and results are presented for the development of the instability, mixing parameters and turbulent kinetic energy spectra. The results are discussed in comparison with previous compressible simulations, theory and experiments.

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Section: Discussionmentioning

confidence: 99%

Computing multi-mode shock-induced compressible turbulent mixing at late times

et al. 2015

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“…The choice of initial conditions build on previous studies [11,13,18,20,21] and have the following features:…”

Section: A Standard Problemmentioning

confidence: 99%

“…Thus a direct comparison of integral properties between all prior studies is not possible. Furthermore, of all prior studies, only four include computations using more than one algorithm for the same initial condition [11,13,14,18], each of them using two independent algorithms. It is not possible to obtain a robust estimate of numerical uncertainty with such a limited sample.…”

Section: Introductionmentioning

confidence: 99%

Late-time growth rate, mixing, and anisotropy in the multimode narrowband Richtmyer–Meshkov instability: The θ-group collaboration

et al. 2017

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Turbulent Richtmyer-Meshkov instability (RMI) is investigated through a series of high resolution three dimensional smulations of two initial conditions with eight independent codes. The simulations are initialised with a narrowband perturbation such that instability growth is due to non-linear coupling/backscatter from the energetic modes, thus generating the lowest expected growth rate from a pure RMI. By independently assessing the results from each algorithm, and computing ensemble averages of multiple algorithms, the results allow a quantification of key flow properties as well as the uncertainty due to differing numerical approaches. A new analytical model predicting the initial layer growth for a multimode narrowband perturbation is presented, along with two models for the linear and non-linear regime combined. Overall, the growth rate exponent is determined as θ = 0.292 ± 0.009, in good agreement with prior studies; however, the exponent is decaying slowly in time. Also, θ is shown to be relatively insensitive to the choice of mixing layer width measurement. The asymptotic integral molecular mixing measures Θ = 0.792 ± 0.014, Ξ = 0.800±0.014 and Ψ = 0.782±0.013 which are lower than some experimental measurements but within the range of prior numerical studies. The flow field is shown to be persistently anisotropic for all algorithms, at the latest time having between 49% and 66% higher kinetic energy in the shock parallel direction compared to perpendicular and does not show any return to isotropy. The plane averaged volume fraction profiles at different time instants collapse reasonably well when scaled by the integral width, implying that the layer can be described by a single length scale and thus a single θ. Quantitative data given for both ensemble averages and individual algorithms provide useful benchmark results for future research.

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“…Previous published direct numerical simulations of RMI include a study by Olson and Greenough [18], as well as the studies of Tritschler et al [19,20].…”

Section: Introductionmentioning

confidence: 99%

“…In [18], single-shock RMI in air and sulphur hexafluoride (SF 6 ) initiated by a Mach 1.18 shock was analysed using two different numerical methods.…”

Section: Introductionmentioning

confidence: 99%

Direct numerical simulation of the multimode narrowband Richtmyer–Meshkov instability

Groom

Thornber

2019

Computers & Fluids

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Early to intermediate time behaviour of the planar Richtmyer-Meshkov instability (RMI) is investigated through direct numerical simulation (DNS) of the evolution of a deterministic interfacial perturbation initiated by a Ma = 1.84 shock. The model problem is the well studied initial condition from the recent θ-group collaboration [Phys. Fluids. 29 (2017) 105107]. A grid convergence study demonstrates that the Kolmogorov microscales are resolved by the finest grid for the entire duration of the simulation, and that both integral and spectral quantities of interest are converged. Compar-isons are made with implicit large eddy simulation (ILES) results from the θ-group collaboration, generated using the same numerical algorithm. The total amount of turbulent kinetic energy (TKE) is shown to be decreased in the DNS compared to the ILES, particularly in the transverse directions, giving rise to a greater level of anisotropy in the flow (70% vs. 40% more TKE in the shock parallel direction at the latest time considered). This decrease in transfer of TKE to the transverse components is shown to be due to the viscous suppression of secondary instabilities. Overall the agreement in the * large scales between the DNS and ILES is very good and hence the mixing width and growth rate exponent θ are very similar. There are substantial differences in the small scale behaviour however, with a 38% difference observed in the minimum values obtained for the mixing fractions Θ and Ξ.Differences in the late time decay of TKE are also observed, with decay rates calculated to be τ −1.41 and τ −1.25 for the DNS and ILES respectively.

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Large eddy simulation requirements for the Richtmyer-Meshkov instability

Cited by 44 publications

References 33 publications

Computing multi-mode shock-induced compressible turbulent mixing at late times

Computing multi-mode shock-induced compressible turbulent mixing at late times

Late-time growth rate, mixing, and anisotropy in the multimode narrowband Richtmyer–Meshkov instability: The θ-group collaboration

Direct numerical simulation of the multimode narrowband Richtmyer–Meshkov instability

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