A return toward equilibrium in a 2D Rayleigh–Taylor instability for compressible fluids with a multidomain adaptive Chebyshev method

Creurer, Benjamin Le; Gauthier, Serge

doi:10.1007/s00162-008-0076-3

Cited by 26 publications

(16 citation statements)

References 51 publications

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“…RTI is encountered in a variety of contexts, such as combustion, inertial-confinement fusion, supernova explosions, and geophysics. Simulations of the compressible RTI are quite common (e.g., see Table 1 of [11] for a list of compressible RTI investigations and other references therein). Furthermore, in a variety of such simulations the Mach number is typically low (O(0.1) or less).…”

Section: Rayleigh-taylor Testmentioning

confidence: 99%

Operator-Based Preconditioning of Stiff Hyperbolic Systems

Reynolds¹,

Samtaney²,

Woodward³

2010

SIAM J. Sci. Comput.

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Abstract.We introduce an operator-based scheme for preconditioning stiff components encountered in implicit methods for hyperbolic systems of PDEs posed on regular grids. The method is based on a directional splitting of the implicit operator, followed by a characteristic decomposition of the resulting directional parts. This approach allows for the solution of any number of characteristic components, from the entire system to only the fastest, stiffness-inducing waves. We apply the preconditioning method to stiff hyperbolic systems arising in magnetohydrodynamics and gas dynamics. We then present numerical results showing that this preconditioning scheme works well on problems where the underlying stiffness results from the interaction of fast transient waves with slowly-evolving dynamics, scales well to large problem sizes and numbers of processors, and allows for additional customization based on the specific problems under study.

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Section: Rayleigh-taylor Testmentioning

confidence: 99%

Operator-Based Preconditioning of Stiff Hyperbolic Systems

Reynolds¹,

Samtaney²,

Woodward³

2010

SIAM J. Sci. Comput.

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“…For whatever reasons, a brief literature survey reveals that a large number of multicomponent NavierStokes simulations omit the enthalpy diffusion term in the energy equation. [21][22][23][24][25][26][27][28][29][30] Here we refer to a Navier-Stokes simulation as any solver that includes viscous, conductive, and diffusive terms, even if those terms represent turbulence models, rather than molecular processes. The primary objective of this paper is to demonstrate some of the errors that can result from neglecting the enthalpy diffusion term and identify some situations in which the term is critically important.…”

Section: Introductionmentioning

confidence: 99%

Enthalpy diffusion in multicomponent flows

Cook

2009

Physics of Fluids

123

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The enthalpy diffusion flux in the multicomponent energy equation is a well-known yet frequently neglected term. It accounts for energy changes associated with compositional changes resulting from species diffusion. The term prevents local violations of the entropy condition in flows where significant mixing occurs between species of dissimilar molecular weight. In simulations of nonpremixed combustion, omission of the enthalpy flux can lead to anomalous temperature gradients, which may cause mixing regions to exceed ignition conditions. The term can also play a role in generating acoustic noise in turbulent mixing layers. Euler solvers that rely on numerical diffusion to blend fluids at the grid scale cannot reliably predict temperatures in mixing regions. On the other hand, Navier-Stokes solvers that incorporate enthalpy diffusion can provide much more accurate results. In constructing turbulence closures for high Reynolds number mixing, the same turbulent diffusion model that appears in the species mass transport equation should also appear in the energy equation as part of a "turbulent enthalpy diffusion;" otherwise the energy and species transport equations will not be consistent.

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“…More recently, Reckinger et al [27] examined single-mode, 2D RTI growth rates for a range of stratification strengths, and Gauthier [15] performed a comprehensive study of the dynamics of multimode, three-dimensional (3D) RTI for a relatively strongly stratified case. Both of these more recent studies employed variable-resolution numerical methods to achieve high Reynolds numbers within the context of fully compressible DNS; Reckinger et al [27] used the parallel adaptive wavelet collocation method (PAWCM) [28] and Gauthier [15] used an auto-adaptive multi-domain Chebyshev-Fourier method [29]. Using currently available computational resources, these and other adaptive techniques are unavoidable when performing fully compressible DNS at high Reynolds numbers.…”

Section: Introductionmentioning

confidence: 99%

Effects of isothermal stratification strength on vorticity dynamics for single-mode compressible Rayleigh-Taylor instability

et al. 2019

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The effects of isothermal stratification strength on vorticity dynamics for single-mode Rayleigh-Taylor instability (RTI) are examined using two dimensional fully compressible wavelet-based direct numerical simulations. The simulations model low Atwood number (A = 0.04) RTI development for four different stratification strengths, corresponding to Mach numbers from 0.3 (weakly stratified) to 1.2 (strongly stratified), and for three different perturbation Reynolds numbers, from 5,000 to 20,000. All simulations use adaptive wavelet-based mesh refinement to achieve very fine spatial resolutions at relatively low computational cost. For all stratifications, the bubble and spike go through the exponential growth regime, followed by a slowing of the RTI evolution. For the weakest stratification, this slow-down is then followed by a re-acceleration, while for stronger stratifications the suppression of RTI growth continues. Bubble and spike asymmetries are observed for weak stratifications, with bubble and spike growth rates becoming increasingly similar as the stratification strength increases. For the range of cases studied, there is relatively little effect of Reynolds number on bubble and spike heights, although the formation of secondary vortices becomes more pronounced as Reynolds number increases. The underlying dynamics are analyzed in detail through an examination of the vorticity transport equation, revealing that incompressible baroclinicity drives RTI growth for small and moderate stratifications, but increasingly leads to the suppression of vorticity production and RTI growth for stronger stratifications. These variations in baroclinicity are used to explain the suppression of RTI growth for strong stratifications, as well as the anomalous asymmetry in bubble and spike growth rates for weak stratifications.

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A return toward equilibrium in a 2D Rayleigh–Taylor instability for compressible fluids with a multidomain adaptive Chebyshev method

Cited by 26 publications

References 51 publications

Operator-Based Preconditioning of Stiff Hyperbolic Systems

Operator-Based Preconditioning of Stiff Hyperbolic Systems

Enthalpy diffusion in multicomponent flows

Effects of isothermal stratification strength on vorticity dynamics for single-mode compressible Rayleigh-Taylor instability

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