A Dynamical Pseudo-Spectral Domain Decomposition Technique: Application to Viscous Compressible Flows

Renaud, François; Gauthier, Serge

doi:10.1006/jcph.1996.5576

Cited by 17 publications

(11 citation statements)

References 27 publications

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“…The solution is thus estimated on this spectral grid with the previously used Runge-Kutta scheme. The subdomain interface locations and the mapping parameters are dynamically adapted by minimizing a norm of the computed solution (Renaud & Gauthier 1997).…”

Section: Resultsmentioning

confidence: 99%

Self-similar solutions of unsteady ablation flows in inertial confinement fusion

2008

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We exhibit and detail the properties of self-similar solutions for inviscid compressible ablative flows in slab symmetry with nonlinear heat conduction which are relevant to inertial confinement fusion (ICF). These solutions have been found after several contributions over the last four decades. We first derive the set of ODEs – a nonlinear eigenvalue problem – which governs the self-similar solutions by using the invariance of the Euler equations with nonlinear heat conduction under the two-parameter Lie group symmetry. A sub-family which leaves the density invariant is detailed since these solutions may be used to model the ‘early-time’ period of an ICF implosion where a shock wave travels from the front to the rear surface of a target. A chart allowing us to determine the starting point of a numerical solution, knowing the physical boundary conditions, has been built. A physical analysis of these unsteady ablation flows is then provided, the associated dimensionless numbers (Mach, Froude and Péclet numbers) being calculated. Finally, we show that self-similar ablation fronts generated within the framework of the above hypotheses (electron heat conduction, growing heat flux at the boundary, etc.) and for large heat fluxes and not too large pressures at the boundary do not satisfy the low-Mach-number criteria. Indeed both the compressibility and the stratification of the hot-flow region are too large. This is, in particular, the case for self-similar solutions obtained for energies in the range of the future Laser MegaJoule laser facility. Two particular solutions of this latter sub-family have been recently used for studying stability properties of ablation fronts.

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Section: Resultsmentioning

confidence: 99%

Self-similar solutions of unsteady ablation flows in inertial confinement fusion

2008

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“…However, too many subdomains may diminish the accuracy. Renaud and Gauthier [47] observed that the best Chebyshev derivation accuracy is obtained for 40 < N z + 1 < 80. Below 40, there are not enough polynomials to get a fine discretization.…”

Section: Results Are Shown Inmentioning

confidence: 97%

“…A simple and robust iterative procedure has been devised for determining the best interface locations and the best values of the mapping parameters ( [47], [46], Section 8.3.4). This algorithm consists in calculating the functional (63) at some selected values around a subdomain interface.…”

Section: Auto-adaptive Multidomain Methodsmentioning

confidence: 99%

“…The variables ( v, p) are solution of a generalized Stokes problem while the velocity v ⊥ , the concentration and the temperature are solution of Helmholtz problems. This Stokes problem is solved by means of both the Uzawa algorithm and the influence matrix method [40,47]. Continuity of the dependent variables and of their first derivatives is required for quantities governed by second-order PDEs, i.e., velocity, temperature and concentration.…”

Section: Numerical Algorithmsmentioning

confidence: 99%

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A spectral anelastic Navier–Stokes solver for a stratified two-miscible-layer system in infinite horizontal channel

Schneider

Hammouch

Labrosse

et al. 2015

Journal of Computational Physics

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“…3(b) encourages us to consider a further simplification, where the exact density and velocity fields of the current front are not required. Following the previous studies [28][29][30], the dispersion relation governed by Eqs. (4)- (7) can be simplified for the semi-infinite fluids with a planar and infinitely thin interface, and the approximate but analytical solution is solved as…”

Section: Lzmentioning

confidence: 98%

Origin of lobe and cleft at the gravity current front

2019

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In this paper the Rayleigh-Taylor instability (RTI) along the density interfaces of gravity-current fronts is analyzed. Both the location and the spanwise wavenumber of the most unstable mode determined by the local dispersion relation agree with those of the strongest perturbation obtained from numerical simulations, suggesting that the original formation mechanism of lobes and clefts at the current front is RTI. Furthermore, the predictions of the semi-infinite RTI model, i.e. the original dominating spanwise wavenumber of the Boussinesq current substantially depends on the Prandtl number and has a 1/3 scaling law with the Grashof number, are confirmed by the three-dimensional numerical simulations.

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A Dynamical Pseudo-Spectral Domain Decomposition Technique: Application to Viscous Compressible Flows

Cited by 17 publications

References 27 publications

Self-similar solutions of unsteady ablation flows in inertial confinement fusion

Self-similar solutions of unsteady ablation flows in inertial confinement fusion

A spectral anelastic Navier–Stokes solver for a stratified two-miscible-layer system in infinite horizontal channel

Origin of lobe and cleft at the gravity current front

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