Numerical analysis of a corrected Smagorinsky model

Siddiqua, Farjana; Xie, Xihui

doi:10.1002/num.22895

Cited by 4 publications

(1 citation statement)

References 34 publications

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“…In the simulation of time-dependent fluid models, various time-stepping schemes have been constructed based on stability and consistency. The backward Euler method, unconditionally stable and easily implemented, can only have first-order accuracy [22,37,52,53]. The trapezoidal rule or two-step backward difference method (BDF2) are both second-order accurate and widely used in computational fluid dynamics [3, 11, 18, 19, 26-29, 43, 48, 55].…”

Section: Introductionmentioning

confidence: 99%

The Semi-implicit DLN Algorithm for the Navier Stokes Equations

Pei

2023

Preprint

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Dahlquist, Liniger, and Nevanlinna design a family of one-leg, two-step meth- ods (the DLN method) that is second order, A− and 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 (avoid- ing 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 dis- sipation criterion are presented to balance the accuracy and computational cost. Numerical tests will be given to support the main conclusions.

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Section: Introductionmentioning

confidence: 99%

The Semi-implicit DLN Algorithm for the Navier Stokes Equations

Pei

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

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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.

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A turbulence model: Model, analysis, and algorithm

Zhang,

Huang

2024

Physics of Fluids

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The standard eddy viscosity model is commonly used to simulate turbulence, but there exist difficulties in simulating the backscatter of the non-statistical equilibrium turbulence. In this work, we construct a novel modified eddy viscosity model based on a simplified Cebeci–Smith equation, which is applied to the non-equilibrium turbulence. Moreover, we analyze some properties of the model and propose a fully discrete scheme, which is proven to be stable and convergent. Finally, some numerical examples are presented to test the theoretical prediction of the proposed scheme, and intermittent backscatter is captured and observed by simulating the established model.

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Numerical analysis of a corrected Smagorinsky model

Cited by 4 publications

References 34 publications

The Semi-implicit DLN Algorithm for the Navier Stokes Equations

The Semi-implicit DLN Algorithm for the Navier Stokes Equations

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

A turbulence model: Model, analysis, and algorithm

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