Backflow stabilization by deconvolution-based large eddy simulation modeling

Xu, Huijuan; Baroli, Davide; Massimo, Francesca Di; Quaini, Annalisa; Veneziani, Alessandro

doi:10.1016/j.jcp.2019.109103

Cited by 13 publications

(6 citation statements)

References 45 publications

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“…Many numerical methods have been developed to approximate the solution of differential equations, e.g., [1,11,32,39,[44][45][46][47]. In complex applications it is however still common to use simple methods, such as the constant time step backward Euler [16,71], the midpoint rule [4,7,18,42,48,68], the trapezoid rule [34,49] or, increasingly, the second-order backward difference (BDF2) method [5,17,28,29,59,78,79,83]. It is well known [67] that for linear multistep methods, unfavorable combinations of variable steps can lead to instability.…”

Section: Related Workmentioning

confidence: 99%

Time step adaptivity in the method of Dahlquist, Liniger and Nevanlinna

Layton

Pei

Trenchea

2023

Preprint

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Dahlquist, Liniger and Nevanlinna devised a family of one-leg two-step methods (DLN) that is second order, A- and G- stable for arbitrary, non-uniform time steps. The DLN method thus has strong potential for use in adaptive codes, but its adaptive step size selection is little explored. This report develops two approaches for the efficient local error estimation in the DLN method, and tests their use in a standard adaptivity framework. Many methods of error estimation are possible; herein we focus on two complementary estimators which involve minimal extra storage and computations. First we evaluate the local truncation error of the DLN method by Milne’s device, using the difference between the solution of the DLN method and the solution of a variable-step, explicit, second-order Adams-Bashforth-like method. Second, we use a recent refactorization of the DLN method, which eases implementation of DLN in legacy codes, to obtain an effective error estimation at no extra cost. We perform a number of numerical tests, comparing the two time adaptive DLN algorithms with some standard numerical ODE packages. Our tests indicate that the adaptive DLN method, with error estimated by Milne’s device, is an efficient and reliable method, even for stiff and unstable problems.

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Section: Related Workmentioning

confidence: 99%

Time step adaptivity in the method of Dahlquist, Liniger and Nevanlinna

Layton

Pei

Trenchea

2023

Preprint

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“…Another classical regularized model is the evolve-filter-relax (EFR) model, which consists of three steps: (i) in the "evolve" step, a standard FOM is used to obtain an intermediate approximation of the velocity; (ii) in the "filter" step, a spatial filter is used to filter (regularize) the intermediate approximation obtained in step (i) and eliminate (alleviate) its spurious numerical oscillations; [4][5][6][7][8][9][10][11][12][13] (iii) in the "relax" step, a more accurate velocity approximation is obtained as a convex combination between the filtered and unfiltered flow approximations. 14,15 The EFR model is a popular regularized model that has been used for different classical numerical methods, for example, the FE method 14,16 and the SE method. 7 The main reasons for the popularity of the EFR model are its simplicity and modularity: given a legacy FOM code, the "evolve" step is already implemented, the "filter" step requires the addition of a simple subroutine, and the "relax" step is just one line of code.…”

Section: Introductionmentioning

confidence: 99%

Consistency of the full and reduced order models for evolve‐filter‐relax regularization of convection‐dominated, marginally‐resolved flows

Strazzullo

Girfoglio

Ballarin

et al. 2022

Numerical Meth Engineering

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Numerical stabilization is often used to eliminate (alleviate) the spurious oscillations generally produced by full order models (FOMs) in under‐resolved or marginally‐resolved simulations of convection‐dominated flows. In this article, we investigate the role of numerical stabilization in reduced order models (ROMs) of marginally‐resolved, convection‐dominated incompressible flows. Specifically, we investigate the FOM–ROM consistency, that is, whether the numerical stabilization is beneficial both at the FOM and the ROM level. As a numerical stabilization strategy, we focus on the evolve‐filter‐relax (EFR) regularization algorithm, which centers around spatial filtering. To investigate the FOM‐ROM consistency, we consider two ROM strategies: (i) the EFR‐noEFR, in which the EFR stabilization is used at the FOM level, but not at the ROM level; and (ii) the EFR‐EFR, in which the EFR stabilization is used both at the FOM and at the ROM level. We compare the EFR‐noEFR with the EFR‐EFR in the numerical simulation of a 2D incompressible flow past a circular cylinder in the convection‐dominated, marginally‐resolved regime. We also perform model reduction with respect to both time and Reynolds number. Our numerical investigation shows that the EFR‐EFR is more accurate than the EFR‐noEFR, which suggests that FOM‐ROM consistency is beneficial in convection‐dominated, marginally‐resolved flows.

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“…The accurate numerical simulation of flows of an incompressible, viscous fluid, with the accompanying complexities occurring in practical settings, is a problem where speed, memory and accuracy never seem sufficient. For time discretization (considered herein), many longer time simulations use constant step low order methods, and (with few exceptions noted in Section 1.1) the remainder use the constant time step implicit midpoint or the trapezoidal schemes, for example, [2,3,8,31,39], (often combined with fractional steps, or with ad hoc fixes to correct for oscillations due to lack of L-stability [6,38,44]), or the backward differentiation formula 2 (BDF2) method [1,18,22,33,34,46]. Time accuracy requires time step adaptivity within the computational, space and cognitive complexity limitations of computational fluid dynamics (CFD).…”

Section: Introductionmentioning

confidence: 99%

Analysis of the variable step method of Dahlquist, Liniger and Nevanlinna for fluid flow

Layton

Pei

Qin

et al. 2021

Numerical Methods Partial

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The one-leg, two-step time discretization proposed by Dahlquist, Liniger and Nevanlinna is second order and variable step G-stable. G-stability for systems of ordinary differential equations (ODEs) corrresponds to unconditional, long time energy stability when applied to the Navier-Stokes equations (NSEs). In this report, we analyze the method of Dahlquist, Liniger and Nevanlinna as a variable step, time discretization of the Navier-Stokes equations. We prove that the kinetic energy is bounded for variable time-steps, show that the method is second-order accurate, characterize its numerical dissipation and prove error estimates. The theoretical results are illustrated by several numerical tests.

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Backflow stabilization by deconvolution-based large eddy simulation modeling

Cited by 13 publications

References 45 publications

Time step adaptivity in the method of Dahlquist, Liniger and Nevanlinna

Time step adaptivity in the method of Dahlquist, Liniger and Nevanlinna

Consistency of the full and reduced order models for evolve‐filter‐relax regularization of convection‐dominated, marginally‐resolved flows

Analysis of the variable step method of Dahlquist, Liniger and Nevanlinna for fluid flow

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