Compressibility effects in Rayleigh–Taylor instability-induced flows

Gauthier, Serge; Creurer, Benjamin Le

doi:10.1098/rsta.2009.0139

Cited by 43 publications

(43 citation statements)

References 71 publications

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“…The added term is zero if the sequence of velocities u n n=0,...,N satisfies the divergence free condition. In (18) we have additionally regularized the problem by adding the term −τ 2 ∆p n+1 , where −∆ is the negative Laplace operator. The purpose of this regularization is to avoid unphysical oscillations in pressure.…”

Section: Algorithm 1 (Bdf2)mentioning

confidence: 99%

Numerical Solution of the Time-Dependent Navier–stokes Equation for Variable Density–variable Viscosity. Part I

Axelsson

Neytcheva

2015

Mathematical Modelling and Analysis

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PostprintThis is the accepted version of a paper published in Mathematical Modelling and Analysis. This paper has been peer-reviewed but does not include the final publisher proof-corrections or journal pagination. AbstractWe consider methods for the numerical simulations of variable density incompressible fluids, modelled by the Navier-Stokes equations. Variable density problems arise, for instance, in interfaces between fluids of different densities in multiphase flows such as appearing in porous media problems. We show that by solving the Navier-Stokes equation for the momentum variable instead of the velocity the corresponding saddle point problem, arising at each time step, no special treatment of the pressure variable is required and leads to an efficient preconditioning of the arising block matrix. This study consists of two parts, of which this paper constitutes Part I. Here we present the algorithm, compare it with a broadly used projection-type method and illustrate some advantages and disadvantages of both techniques via analysis and numerical experiments. In addition we also include test results for a method, based on coupling of the Navier-Stokes equations with a phase-field model, where the variable density function is handled in a different way.The theory including stability bounds and a second order splitting method is dealt with in Part II of the study.

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Section: Algorithm 1 (Bdf2)mentioning

confidence: 99%

Numerical Solution of the Time-Dependent Navier–stokes Equation for Variable Density–variable Viscosity. Part I

Axelsson

Neytcheva

2015

Mathematical Modelling and Analysis

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“…For compressible materials, especially in high energy density plasmas, the condition (4) should also be augmented with other considerations [24][25][26] . Note also that a finite equilibrium pressure should be maintained by the material or by the magnetic field in order for RTI to develop.…”

Section: Potential Development Of Rayleigh-taylor Instabilitiesmentioning

confidence: 99%

Tendency of spherically imploding plasma liners formed by merging plasma jets to evolve toward spherical symmetry

et al. 2012

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Three dimensional hydrodynamic simulations have been performed using smoothed particle hydrodynamics (SPH) in order to study the effects of discrete jets on the processes of plasma liner formation, implosion on vacuum, and expansion. The pressure history of the inner portion of the liner was qualitatively and quantitatively similar from peak compression through the complete stagnation of the liner among simulation results from two one dimensional radiationhydrodynamic codes, 3D SPH with a uniform liner, and 3D SPH with 30 discrete plasma jets.Two dimensional slices of the pressure show that the discrete jet SPH case evolves towards a profile that is almost indistinguishable from the SPH case with a uniform liner, showing that non-uniformities due to discrete jets are smeared out by late stages of the implosion. Liner formation and implosion on vacuum was also shown to be robust to Rayleigh-Taylor instability growth. Interparticle mixing for a liner imploding on vacuum was investigated. The mixing rate was very small until after peak compression for the 30 jet simulation.

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“…The paradigms of turbulent mixing considered in this collection are the passive scalar mixing (Sreenivasan & Schumacher 2010) and mixing induced by hydrodynamic instabilities, including Rayleigh-Taylor (RT) and RichtmyerMeshkov (RM) (Abarzhi 2010;Aglitskiy et al 2010;Andrews & Dalziel 2010;Gauthier & Creurer 2010;Kadau et al 2010;Nishihara et al 2010). The passive scalar problem is standard, but the focus in this issue is the Lagrangian approach.…”

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Turbulent mixing and beyond

Abarzhi

Sreenivasan

2010

Phil. Trans. R. Soc. A.

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Turbulence is a supermixer. Turbulent mixing has immense consequences for physical phenomena spanning astrophysical to atomistic scales under both high-and lowenergy-density conditions. It influences thermonuclear fusion in inertial and magnetic confinement systems; governs dynamics of supernovae, accretion disks and explosions; dominates stellar convection, planetary interiors and mantle-lithosphere tectonics; affects premixed and non-premixed combustion; controls standard turbulent flows (wall-bounded and free-subsonic, supersonic as well as hypersonic); as well as atmospheric and oceanic phenomena (which themselves have important effects on climate). In most of these circumstances, the mixing phenomena are driven by non-equilibrium dynamics. While each article in this collection dwells on a specific problem, the purpose here is to seek a few unified themes amongst diverse phenomena.Keywords: turbulent mixing; passive scalars; Rayleigh-Taylor instability; Richtmyer-Meshkov instability; high-energy-density physics; holographic technologies Compared with the vast variety of physical circumstances in which turbulent mixing occurs, our knowledge of it is still limited. The problem is relatively straightforward for a simple velocity field (e.g. a constant or periodic in two dimensions), but very few rigorous results exist if the fluid mixing is threedimensional and fully turbulent. The case we do understand better, though incompletely, is the mixing of a passive scalar in isotropic and homogeneous turbulence at high Reynolds numbers, for which sound phenomenological understanding exists (e.g. Obukhov 1949;Yaglom 1949;Corrsin 1951;Batchelor 1959;Kraichnan 1968).Most realistic mixing problems in nature and technology are more complex than passive scalar mixing and involve strong gradients of pressure and density, heat release, transfer of species and changes in chemical composition. Remington et al. 2006). These phenomena are essentially anisotropic, involve non-local interactions among the many scales constituting the physical phenomena, as well as phase changes of matter, and are often driven by shocks or acceleration. In continuum approximation, their scaling laws, spectral shapes and invariant properties differ substantially from those of classical Kolmogorov (1941) turbulence. Singular aspects and similarity of their dynamics are interplayed with the fundamental properties of the Euler and Navier-Stokes equations (Ladyzhenskaya 1975;Scheffer 1976). In the kinetic limit, the non-equilibrium dynamics depart qualitatively from the standard scenario of the Gibbs ensemble and the Boltzmann weight (Hoover 1991;Evans & Morriss 2008). There is thus a strong need for advancing new theoretical methods well beyond the idealized (e.g. isotropic, homogeneous and statistically steady) domain.The state-of-the-art numerical simulations have the potential for developing predictive modelling of the multi-scale non-equilibrium mixing dynamics. With computational power doubling every 18 months or so, larger simulations involving g...

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Compressibility effects in Rayleigh–Taylor instability-induced flows

Cited by 43 publications

References 71 publications

Numerical Solution of the Time-Dependent Navier–stokes Equation for Variable Density–variable Viscosity. Part I

Numerical Solution of the Time-Dependent Navier–stokes Equation for Variable Density–variable Viscosity. Part I

Tendency of spherically imploding plasma liners formed by merging plasma jets to evolve toward spherical symmetry

Turbulent mixing and beyond

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