Stability Analysis for an Interface with a Continuous Internal Structure

Modestov, Mikhail

doi:10.3390/fluids6010018

Cited by 2 publications

(1 citation statement)

References 15 publications

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“…Taking into account the finite thickness of the transition layer may allow additional instabilities and algebraically growing solutions that the present method is oblivious of. 45,46 Other uses of such methods may conceivably be found in computational fluid dynamics and acoustics. For simulation post-processing, one could tag discontinuities and examine their spectral properties a posteriori, or track wave packets in a Monte-Carlo fashion as they are punctually refracted.…”

Section: Ambipolar Diffusionmentioning

confidence: 99%

Normal mode analysis of fluid discontinuities: Numerical method and application to magnetohydrodynamics

Béthune

2023

Physics of Fluids

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Fluid discontinuities, such as shock fronts and vortex sheets, can reflect waves and become unstable to corrugation. Analytical calculations of these phenomena are tractable in the simplest cases only, while their numerical simulations are biased by truncation errors inherent to discretization schemes. The author lays down a computational framework to study the coupling of normal modes (plane linear waves) through discontinuities satisfying arbitrary conservation laws, as is relevant to a variety of fluid mechanical problems. A systematic method is provided to solve these problems numerically, along with a series of validation cases. As a demonstration, it is applied to magnetohydrodynamic shocks and shear layers to exactly recover their linear stability properties. The straightforward inclusion of nonideal (dispersive, dissipative) effects notably opens a route to investigate how these phenomena are altered in weakly ionized plasmas.

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Section: Ambipolar Diffusionmentioning

confidence: 99%

Normal mode analysis of fluid discontinuities: Numerical method and application to magnetohydrodynamics

Béthune

2023

Physics of Fluids

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Effect of momentum and heat losses on the hydrodynamic instability of a premixed equidiffusive flame in a Hele–Shaw cell

2021

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The linear stage of hydrodynamic instability of a laminar premixed flame propagating in a Hele–Shaw cell is investigated. Our theoretical model takes into account momentum and heat losses, temperature-dependent transport coefficients, and the continuous internal structure of the flame front. The dispersion relation is obtained numerically as a solution to an eigenvalue problem for the linearized governing equations. The obtained results are in good qualitative and quantitative agreement with previous studies. It is shown that the wall heat losses tend to weaken the hydrodynamic flame instability. On the contrary, momentum losses enhance the flame instability. It is demonstrated that for the adiabatic walls, an increase in the Hele–Shaw cell width results in a reduction of the instability growth rate. For the non-adiabatic walls, there is a competition between momentum and heat losses in narrow channels that may result in a non-monotonic dependence of the instability growth rate on the Hele–Shaw cell width. It is shown that the effects of the Prandtl number and the thermal expansion vary with the wall heat loss coefficient. A possibility of non-monotonic dependence of the maximum instability growth rate on the thermal expansion has been demonstrated.

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Stability Analysis for an Interface with a Continuous Internal Structure

Cited by 2 publications

References 15 publications

Normal mode analysis of fluid discontinuities: Numerical method and application to magnetohydrodynamics

Normal mode analysis of fluid discontinuities: Numerical method and application to magnetohydrodynamics

Effect of momentum and heat losses on the hydrodynamic instability of a premixed equidiffusive flame in a Hele–Shaw cell

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