Numerical Investigation of Single-Mode Richtmyer-Meshkov Instability

2005 ◽  
Author(s):  
Nicholas Mueschke ◽  
Wayne N. Kraft ◽  
Odion Dibua ◽  
Malcolm J. Andrews ◽  
Jeffrey W. Jacobs
Keyword(s):  
Initial Velocity ◽  
Single Mode ◽  
Incompressible Fluids ◽  
Late Time ◽  
Two Dimensional ◽  
Time Step ◽  
Incompressible Media ◽  
Velocity Impulse ◽  
Acceleration History ◽  
Flux Limiters

The Richtmyer-Meshkov (RM) instability occurs when a shock passes through a perturbed interface separating fluids of different densities. Similarly, RM instabilities may also occur when a perturbed interface between two incompressible fluids of different density is impulsively accelerated. We report work that investigates RM instabilities between incompressible media by way of numerical simulations that are matched to experiments reported by Niederhaus & Jacobs [1]. We also describe a compact, fractional time-step, two-dimensional, finite-volume numerical algorithm that solves the non-Bousinesq Euler equations explicitly on a Cartesian, co-located grid. Numerical advection of volume fractions and momentum is second-order accurate in space and unphysical oscillations are prevented by using Van Leer flux limiters [2,3]. An initial velocity impulse has been used to model the impulsive acceleration history found in the experiments [1]. We report accurate simulation of the experimentally measured early-, intermediate-, and late-time penetrations of one fluid into another.

scholarly journals Rarefaction-driven Rayleigh–Taylor instability. Part 2. Experiments and simulations in the nonlinear regime

2018 ◽  
Vol 838 ◽  
pp. 320-355 ◽  
Author(s):  
R. V. Morgan ◽  
W. H. Cabot ◽  
J. A. Greenough ◽  
J. W. Jacobs
Keyword(s):  
Rarefaction Wave ◽  
Three Dimensional ◽  
Single Mode ◽  
Taylor Instability ◽  
Nonlinear Regime ◽  
Diffuse Interface ◽  
Late Time ◽  
Two Dimensional ◽  
Rayleigh Taylor Instability ◽  
Atwood Number

Experiments and large eddy simulation (LES) were performed to study the development of the Rayleigh–Taylor instability into the saturated, nonlinear regime, produced between two gases accelerated by a rarefaction wave. Single-mode two-dimensional, and single-mode three-dimensional initial perturbations were introduced on the diffuse interface between the two gases prior to acceleration. The rarefaction wave imparts a non-constant acceleration, and a time decreasing Atwood number, $A=(\unicode[STIX]{x1D70C}_{2}-\unicode[STIX]{x1D70C}_{1})/(\unicode[STIX]{x1D70C}_{2}+\unicode[STIX]{x1D70C}_{1})$, where $\unicode[STIX]{x1D70C}_{2}$ and $\unicode[STIX]{x1D70C}_{1}$ are the densities of the heavy and light gas, respectively. Experiments and simulations are presented for initial Atwood numbers of $A=0.49$, $A=0.63$, $A=0.82$ and $A=0.94$. Nominally two-dimensional (2-D) experiments (initiated with nearly 2-D perturbations) and 2-D simulations are observed to approach an intermediate-time velocity plateau that is in disagreement with the late-time velocity obtained from the incompressible model of Goncharov (Phys. Rev. Lett., vol. 88, 2002, 134502). Reacceleration from an intermediate velocity is observed for 2-D bubbles in large wavenumber, $k=2\unicode[STIX]{x03C0}/\unicode[STIX]{x1D706}=0.247~\text{mm}^{-1}$, experiments and simulations, where $\unicode[STIX]{x1D706}$ is the wavelength of the initial perturbation. At moderate Atwood numbers, the bubble and spike velocities approach larger values than those predicted by Goncharov’s model. These late-time velocity trends are predicted well by numerical simulations using the LLNL Miranda code, and by the 2009 model of Mikaelian (Phys. Fluids., vol. 21, 2009, 024103) that extends Layzer type models to variable acceleration and density. Large Atwood number experiments show a delayed roll up, and exhibit a free-fall like behaviour. Finally, experiments initiated with three-dimensional perturbations tend to agree better with models and a simulation using the LLNL Ares code initiated with an axisymmetric rather than Cartesian symmetry.

scholarly journals Late-time growth of the Richtmyer–Meshkov instability for different Atwood numbers and different dimensionalities

2003 ◽  
Vol 21 (3) ◽  
pp. 363-368 ◽  
Author(s):  
A. YOSEF-HAI ◽  
O. SADOT ◽  
D. KARTOON ◽  
D. ORON ◽  
L.A. LEVIN ◽  
...  
Keyword(s):  
Growth Rate ◽  
Theoretical Model ◽  
Numerical Simulations ◽  
Initial Perturbation ◽  
Three Dimensional ◽  
Single Mode ◽  
Late Time ◽  
Two Dimensional ◽  
Good Agreement

The late-time growth rate of the Richtmyer–Meshkov instability was experimentally studied at different Atwood numbers with two-dimensional (2D) and three-dimensional (3D) single-mode initial perturbations. The results of these experiments were found to be in good agreement with the results of the theoretical model and numerical simulations. In another set of experiments a bubble-competition phenomenon, which was observed in previous work for 2D initial perturbation (Sadotet al., 1998), was shown to exist also when the initial perturbation is of a 3D nature.

scholarly journals A two-dimensional glacier–fjord coupled model applied to estimate submarine melt rates and front position changes of Hansbreen, Svalbard

2018 ◽  
Vol 64 (247) ◽  
pp. 745-758 ◽  
Author(s):  
E. DE ANDRÉS ◽  
J. OTERO ◽  
F. NAVARRO ◽  
A. PROMIŃSKA ◽  
J. LAPAZARAN ◽  
...  
Keyword(s):  
Coupled Model ◽  
Small Scale ◽  
Two Dimensional ◽  
Time Step ◽  
Software Packages ◽  
Front Position ◽  
Circulation Patterns ◽  
Glacier Front ◽  
Order Of Magnitude ◽  
Frontal Ablation

ABSTRACTWe have developed a two-dimensional coupled glacier–fjord model, which runs automatically using Elmer/Ice and MITgcm software packages, to investigate the magnitude of submarine melting along a vertical glacier front and its potential influence on glacier calving and front position changes. We apply this model to simulate the Hansbreen glacier–Hansbukta proglacial–fjord system, Southwestern Svalbard, during the summer of 2010. The limited size of this system allows us to resolve some of the small-scale processes occurring at the ice–ocean interface in the fjord model, using a 0.5 s time step and a 1 m grid resolution near the glacier front. We use a rich set of field data spanning the period April–August 2010 to constrain, calibrate and validate the model. We adjust circulation patterns in the fjord by tuning subglacial discharge inputs that best match observed temperature while maintaining a compromise with observed salinity, suggesting a convectively driven circulation in Hansbukta. The results of our model simulations suggest that both submarine melting and crevasse hydrofracturing exert important controls on seasonal frontal ablation, with submarine melting alone not being sufficient for reproducing the observed patterns of seasonal retreat. Both submarine melt and calving rates accumulated along the entire simulation period are of the same order of magnitude, ~100 m. The model results also indicate that changes in submarine melting lag meltwater production by 4–5 weeks, which suggests that it may take up to a month for meltwater to traverse the englacial and subglacial drainage network.

Design of optical coupling systems between two-dimensional quasi-stadium laser diodes and single-mode optical fibers

2009 ◽  
Vol 16 (5) ◽  
pp. 540-547 ◽  
Author(s):  
Takehiro Fukushima ◽  
Yoshiyuki Handa ◽  
Kunihiro Miyahara
Keyword(s):  
Optical Fibers ◽  
Laser Diodes ◽  
Single Mode ◽  
Optical Coupling ◽  
Two Dimensional

Enhanced Explicit Scheme to Solve Transient Heat Conduction Problem

2007 ◽  
Vol 2 (1) ◽  
Author(s):  
Ganesh Hegde ◽  
Madhu Gattumane
Keyword(s):  
Heat Conduction ◽  
Correction Factor ◽  
Truncation Error ◽  
Transient Heat Conduction ◽  
Explicit Scheme ◽  
Stability And Convergence ◽  
Two Dimensional ◽  
Time Step ◽  
One Dimensional ◽  
Partial Derivatives

Improvement in accuracy without sacrificing stability and convergence of the solution to unsteady diffusion heat transfer problems by computational method of enhanced explicit scheme (EES), has been achieved and demonstrated, through transient one dimensional and two dimensional heat conduction. The truncation error induced in the explicit scheme using finite difference technique is eliminated by optimization of partial derivatives in the Taylor series expansion, by application of interface theory developed by the authors. This theory, in its simple terms gives the optimum values to the decision vectors in a redundant linear equation. The time derivatives and the spatial partial derivatives in the transient heat conduction, take the values depending on the time step chosen and grid size assumed. The time correction factor and the space correction factor defined by step sizes govern the accuracy, stability and convergence of EES. The comparison of the results of EES with analytical results, show decreased error as compared to the result of explicit scheme. The paper has an objective of reducing error in the explicit scheme by elimination of truncation error introduced by neglecting the higher order terms in the expansion of the governing function. As the pilot examples of the exercise, the implementation is aimed at solving one-dimensional and two-dimensional problems of transient heat conduction and compared with the results cited in the referred literature.

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