A two-step stabilized finite element algorithm for the Smagorinsky model

Zheng, Bo; Shang, Yueqiang

doi:10.1016/j.amc.2022.126971

Cited by 3 publications

(1 citation statement)

References 28 publications

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“…In Shi et al [15], a low-order nonconforming mixed FEM for the Smagorinsky model was studied. In Zheng and Shang [16], a two-step stabilized FEM for solving the Smagorinsky model was established.…”

Section: Introductionmentioning

confidence: 99%

Error estimates of a two‐grid penalty finite element method for the Smagorinsky model

Yang

2023

Math Methods in App Sciences

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In the paper, we consider the penalty finite element methods (FEMs) for the stationary Smagorinsky model. Firstly, a one‐grid penalty FEM is proposed and analyzed. Since this method is nonlinear, a novel linearized iteration scheme is derived for solving it. We also derived the stability and convergence of numerical solutions for this iteration scheme. Furthermore, a two‐grid penalty FEM is developed for Smagorinsky model. Under , this method consist of solving a nonlinear Smagorinsky model by the one‐grid penalty FEM with the proposed linearized iteration scheme on a coarse mesh with mesh width and then solving a linearized Smagorinsky model based on the Newton iteration on a fine mesh with mesh width , respectively. Stability and error estimates of numerical solutions for two‐grid penalty FEM are presented. Finally, some numerical tests are provided to confirm the theoretical analysis and the effectiveness of the developed methods.

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Section: Introductionmentioning

confidence: 99%

Error estimates of a two‐grid penalty finite element method for the Smagorinsky model

Yang

2023

Math Methods in App Sciences

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Numerical simulation of interfacial resonant Faraday waves between two immiscible liquids

Liu,

Jiang,

Lin

2024

Physics of Fluids

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An in-house numerical model is extended to study the resonant Faraday waves at the interface between two immiscible liquids with the consideration of surface tension. The surface tension module was first added in this model and validated by two standard tests, i.e., the development of a non-equilibrium liquid droplet with square shape and the development of Rayleigh–Taylor instability on the interface of two fluids with different densities. Two experiments were conducted to investigate the resonant Faraday waves at the interface of two liquids in a tank under vertical excitation. The numerical results are compared with the experimental data in terms of wave profiles, and favorable agreements are obtained. It has been found that only when the surface tension is properly taken into account, the numerical model can describe the resonant Faraday waves satisfactorily, especially for the secondary interfacial instability and the wave breaking between two immiscible liquids. In addition, the comparisons between numerical results for different surface tensions indicate that the surface tension plays an important stabilizing role during the development of interfacial Faraday waves and the subsequent secondary instability, and the existence of surface tension can help prevent the flow structures transforming from two-dimensional to three-dimensional.

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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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A two-step stabilized finite element algorithm for the Smagorinsky model

Cited by 3 publications

References 28 publications

Error estimates of a two‐grid penalty finite element method for the Smagorinsky model

Error estimates of a two‐grid penalty finite element method for the Smagorinsky model

Numerical simulation of interfacial resonant Faraday waves between two immiscible liquids

A turbulence model: Model, analysis, and algorithm

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