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Open AccessArticle

A Relaxation Filtering Approach for Two-Dimensional Rayleigh–Taylor Instability-Induced Flows

School of Mechanical and Aerospace Engineering, Oklahoma State University, Stillwater, OK 74078, USA
Author to whom correspondence should be addressed.
Fluids 2019, 4(2), 78;
Received: 12 February 2019 / Revised: 10 April 2019 / Accepted: 16 April 2019 / Published: 21 April 2019
(This article belongs to the Special Issue Multiscale Turbulent Transport)
PDF [16829 KB, uploaded 14 May 2019]


In this paper, we investigate the performance of a relaxation filtering approach for the Euler turbulence using a central seven-point stencil reconstruction scheme. High-resolution numerical experiments are performed for both multi-mode and single-mode inviscid Rayleigh–Taylor instability (RTI) problems in two-dimensional canonical settings. In our numerical assessments, we focus on the computational performance considering both time evolution of the flow field and its spectral resolution up to three decades of inertial range. Our assessments also include an implicit large eddy simulation (ILES) approach that is based on a fifth-order weighted essential non-oscillatory (WENO) with built-in numerical dissipation due to its upwind-based reconstruction architecture. We show that the relaxation filtering approach equipped with a central seven-point stencil, sixth-order accurate discrete filter yields accurate results efficiently, since there is no additional cost associated with the computation of the smoothness indicators and interface Riemann solvers. Our a-posteriori spectral analysis also demonstrates that its resolution capacity is sufficiently high to capture the details of the flow behavior induced by the instability. Furthermore, its resolution capability can be effectively controlled by the filter shape and strength. View Full-Text
Keywords: Rayleigh–Taylor instability; relaxation filtering; implicit LES; WENO schemes; Euler equations Rayleigh–Taylor instability; relaxation filtering; implicit LES; WENO schemes; Euler equations

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Rahman, S.M.; San, O. A Relaxation Filtering Approach for Two-Dimensional Rayleigh–Taylor Instability-Induced Flows. Fluids 2019, 4, 78.

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