An AFC-stabilized implicit finite element method for partial differential equations on evolving-in-time surfaces

Sokolov, A. Yu.; Ali, Ramzan; Turek, Stefan

doi:10.1016/j.cam.2015.03.002

Cited by 50 publications

(22 citation statements)

References 42 publications

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“…The approach of LBM for solving governing PDEs is different as compared to traditional numerical techniques. 25,27 In Lattice Boltzmann method eight particles move from one lattice node to other in their respective directions. These particles also collide with each other and change their velocity directions.…”

Section: B Lattice Boltzmann Methods (Lbm)mentioning

confidence: 99%

Numerical investigation of fluid-solid interaction for flow around three square cylinders

et al. 2018

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In this work, fluid-solid interactions are numerically investigated for flow around three equally/unequally spaced square cylinders using the lattice Boltzmann method. Two major trends of shear layers observed for equal gap spacings between cylinders: (i) without roll up (W), and (ii) with roll up (R). While for unequal gap spacings, four major trends of shear layers observed: (i) without roll up in both gaps (WW), (ii) without rollup in first gap and with roll up in second gap (WR), (iii) with roll up in first gap and without roll up in second gap (RW), and (iv) with roll up in both gaps (RR). g = 3 is found to be the critical equal spacing value. Also g = 1.5 is found to be suitable equal spacing in terms of minimum drag force. While the suitable unequal gap spacing combinations found in this study are (g1, g2) = (1.5, 0.5), (g1, g2) = (3, 0.5) and (g1, g2) = (5, 0.5). Results show that flow induced forces can be suppressed by suitable unequal gap spacing combinations.

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Section: B Lattice Boltzmann Methods (Lbm)mentioning

confidence: 99%

Numerical investigation of fluid-solid interaction for flow around three square cylinders

et al. 2018

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“…(ii) In particular from (18) we see that under the assumption (11) the inequality (17) already implies (16).…”

Section: Proof (I) We Remark Thatmentioning

confidence: 92%

“…For the numerical treatment of reaction-diffusion systems on evolving surfaces we refer to [15,16] in the case of surface finite element methods and to [17] for a level set approach. Moreover, we would like to point a recent contribution on a level set method for reaction-advection-diffusion systems on time dependent surfaces [18].…”

Section: Introductionmentioning

confidence: 99%

Turing-type instabilities in bulk–surface reaction–diffusion systems

Rätz

2015

Journal of Computational and Applied Mathematics

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a b s t r a c tIn this contribution we consider a coupled bulk-surface reaction-diffusion system and for infinitely fast bulk diffusion its formal reduction to a non-local surface PDE model. Thereby, we review results of linear stability analyses for both models showing that Turingtype instabilities can occur for equal lateral diffusion coefficients. The stability results are confirmed by new numerical results. As a specific application, we study a model for a spatial and reaction cycle of signalling molecules in a cell.

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“…The fluid is heated by fluid friction, whereas the heat conduction acts as a heat sink and decreases the temperature increase in the fluid. The transient energy equation for the liquid film that ignores compression and radiation is expressed as [25][26][27][28][29] FIG. 7.…”

Section: Mathematical Model and Simulation Of Temperaturementioning

confidence: 99%

The effect of energy accumulation and boundary slip on laminar flow between rotating plates

Zeng

Chen

et al. 2018

AIP Advances

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The poor operating conditions of fluid lubrication equipment during the start-up process are due to the resistance of the high-viscosity lubricating liquid. Moreover, the excessive reduction in fluid viscosity due to the elevated temperature resulting from power consumption during prolonged operation is not conducive to the generation of dynamic pressure. In this study, we examine the effect of energy accumulation and boundary slip on the laminar flow of a liquid between a pair of rotating plates. The experiments are conducted using a rotary rheometer, with polymethyl methacrylate (PMMA) as the thermal insulation material and polytetrafluoroethylene (PTFE) as the slip drag reduction material, and a three-dimensional simulation model is established. This model is derived by combining the energy equation including the slip length and the heat conduction equation. Thus, the temperature changes over time are predicted by this model, and the model accuracy is verified by experiments. The results reveal the following points: 1) boundary slips function as a drag reduction mechanism for short-time continuous operation; 2) under prolonged operation, the slip reduces the extent of the oil viscosity decrease and clear control of the elevated temperature by the boundary slip is observed.

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An AFC-stabilized implicit finite element method for partial differential equations on evolving-in-time surfaces

Cited by 50 publications

References 42 publications

Numerical investigation of fluid-solid interaction for flow around three square cylinders

Numerical investigation of fluid-solid interaction for flow around three square cylinders

Turing-type instabilities in bulk–surface reaction–diffusion systems

The effect of energy accumulation and boundary slip on laminar flow between rotating plates

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