Second‐order efficient nonlinear filter stabilization for high Reynolds number flows

Takhirov, Aziz; Trenchea, Catalin; Waters, Jiajia

doi:10.1002/num.22859

Cited by 3 publications

(1 citation statement)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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

View full text Add to dashboard Cite

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.

show abstract

Section: Related Workmentioning

confidence: 99%

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

Layton

Pei

Trenchea

2023

Preprint

View full text Add to dashboard Cite

show abstract

The semi-implicit DLN algorithm for the Navier-Stokes equations

Pei

2024

Numer Algor

View full text Add to dashboard Cite

Dahlquist, Liniger, and Nevanlinna design a family of one-leg, two-step methods (the DLN method) that is second order, $$\varvec{A}-$$ A - and $$\varvec{G}-$$ G - stable for arbitrary, non-uniform time steps. Recently, the implementation of the DLN method can be simplified by the refactorization process (adding time filters on the backward Euler scheme). Due to these fine properties, the DLN method has strong potential for the numerical simulation of time-dependent fluid models. In the report, we propose a semi-implicit DLN algorithm for the Navier-Stokes equations (avoiding non-linear solver at each time step) and prove the unconditional, long-term stability, and second-order convergence with the moderate time step restriction. Moreover, the adaptive DLN algorithms by the required error or numerical dissipation criterion are presented to balance the accuracy and computational cost. Numerical tests will be given to support the main conclusions.

show abstract

Efficient nonlinear filter stabilization of the Leray-α model

Takhirov

Trenchea²

2022

Journal of Computational Physics

View full text Add to dashboard Cite

Second‐order efficient nonlinear filter stabilization for high Reynolds number flows

Cited by 3 publications

References 35 publications

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

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

The semi-implicit DLN algorithm for the Navier-Stokes equations

Efficient nonlinear filter stabilization of the Leray-α model

Contact Info

Product

Resources

About