Residual-based variational multiscale simulation of free surface flows

Lins, Erb F.; Elias, Renato N.; Rochinha, Fernando A.; Coutinho, Álvaro L. G. A.

doi:10.1007/s00466-010-0495-z

Cited by 28 publications

(22 citation statements)

References 58 publications

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“…Differences between RBVMS and LES solutions can be observed in Figure that features the velocity field in the middle plane. It is also worth mentioning that the computational performance of the time evolution nonlinear solvers employed in both formulations are quite similar, as observed previously in and .…”

Section: Results and Analysessupporting

confidence: 77%

“…We may define then the τ ′ s , where h e is the element length computed here simply as the cubic root of the element volume, Δ t is the time step and c 1 and c 2 are mesh‐independent algorithmic constants as,

τ_{m} MathClass-rel= {((), {((), \frac{2}{Δt})}^{2} MathClass-bin+ {((), c_{1} \frac{(∥∥, {bold-italicu}^{h})}{h_{e}})}^{2} MathClass-bin+ {((), c_{2} \frac{ν}{h_{e}^{2}})}^{2})}^{MathClass-bin- \frac{1}{2}} τ_{c} MathClass-rel= \frac{h_{e}}{3} (∥∥, {bold-italicu}^{h})

τ_{t} MathClass-rel= {((), {((), \frac{2}{Δt})}^{2} MathClass-bin+ {((), c_{1} \frac{(∥∥, {bold-italicu}^{h})}{h_{e}})}^{2} MathClass-bin+ {((), c_{2} \frac{k}{h_{e}^{2}})}^{2})}^{MathClass-bin- \frac{1}{2}}

the previous definitions are usual in the literature and the presence of the time step is alleged to bring numerical instability. A remedy is to use parameters computed on element–vector‐based definitions as in or impose (adaptively or not) a CFL condition into the mesh, which eliminates the transient term in the previous definitions .…”

Section: Governing Equationsmentioning

confidence: 99%

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Numerical simulation of particle‐laden flows by the residual‐based variational multiscale method

Guerra

Zio

Camata

et al. 2013

Numerical Methods in Fluids

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SUMMARYWe present a finite element residual‐based variational multiscale formulation applied to the numerical simulation of particle‐laden flows. We employ a Eulerian–Eulerian framework to describe the flows in which the mathematical model results from the incompressible Navier–Stokes equation combined with an advection–diffusion transport equation. Special boundary conditions at the bottom are introduced to take into account sediments deposition. Computational experiments are organized in two examples. The first example deals with the well‐known gravity current benchmark, the lock‐exchange configuration. The second also employs for the current initiation the lock configuration, but the sediment particles are endowed with a deposition velocity and are allowed to leave the domain in the moment they reach the bottom. This is intended to mimic, partially, as the bed morphology is not allowed to change, the deposition process, in which sediment deposits are no longer carried by the flow. The spatial pattern of the deposition and its correlation with flow structures are the main focus of this analysis. Numerical experiments have shown that the present formulation captures most of the relevant turbulent flow features with reasonable accuracy, when compared with highly resolved numerical simulations and experimental data. Copyright © 2013 John Wiley & Sons, Ltd.

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Section: Results and Analysessupporting

confidence: 77%

τ_{m} MathClass-rel= {((), {((), \frac{2}{Δt})}^{2} MathClass-bin+ {((), c_{1} \frac{(∥∥, {bold-italicu}^{h})}{h_{e}})}^{2} MathClass-bin+ {((), c_{2} \frac{ν}{h_{e}^{2}})}^{2})}^{MathClass-bin- \frac{1}{2}} τ_{c} MathClass-rel= \frac{h_{e}}{3} (∥∥, {bold-italicu}^{h})

τ_{t} MathClass-rel= {((), {((), \frac{2}{Δt})}^{2} MathClass-bin+ {((), c_{1} \frac{(∥∥, {bold-italicu}^{h})}{h_{e}})}^{2} MathClass-bin+ {((), c_{2} \frac{k}{h_{e}^{2}})}^{2})}^{MathClass-bin- \frac{1}{2}}

Section: Governing Equationsmentioning

confidence: 99%

Numerical simulation of particle‐laden flows by the residual‐based variational multiscale method

Guerra

Zio

Camata

et al. 2013

Numerical Methods in Fluids

Self Cite

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“…We variationally project the model for v II onto the level-I problem (24)- (25), which can be expressed as:…”

Section: Coarse Scalesmentioning

confidence: 99%

“…In this approach, the computational mesh is fixed and the location of the free surface is traced employing an additional scalar field. One of the first applications of this method is the volume of fluids (VOF) technique, 12,16,25 which uses a scalar field that represents the fraction of fluid in each of the mesh elements. Another interface capturing technique is the level set method 1,22,24,39 in which an additional field is introduced to capture the evolving interface.…”

Section: Introductionmentioning

confidence: 99%

Residual-based turbulence models and arbitrary Lagrangian–Eulerian framework for free surface flows

Calderer

Zhu

Gibson

et al. 2015

Math. Models Methods Appl. Sci.

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Communicated by K. TakizawaWe present a residual-based turbulence model for problems with free surfaces. The method is derived based on variational multiscale ideas that assume a decomposition of the solution fields into overlapping scales that are termed as coarse and fine scales. The fine scales are further split hierarchically into fine-scales level-I and fine-scales level-II. The hierarchical variational problems that govern the two fine-scale components are modeled employing bubble functions approach. The model for level-II scales is variationally embedded in the mixed field level-I problem to yield a stable level-I formulation. Subsequently, the model for level-I scales that in fact constitutes the fine-scale turbulence model is then variationally injected in the coarse-scale variational form. A significant feature of the method is that it does not contain any embedded tunable parameters. To accommodate the moving boundaries we cast the formulation in an arbitrary Lagrangian-Eulerian frame of reference. The free surface boundary condition is imposed weakly which results in a formulation that conserves the volume of the fluid. A variety of benchmark problems show the accuracy and range of applicability of the proposed formulation and results are compared with published data. A wavy bed problem is investigated to show the interaction of turbulence generated at the bottom surface with the free surface thereby leading to irregular free surface elevations. Keywords: Irregular free surfaces; open channel; residual-based turbulence models; variational multiscale method; large eddy simulation. † Corresponding author 1 Math. Models Methods Appl. Sci. Downloaded from www.worldscientific.com by UNIVERSITY OF PITTSBURGH on 08/18/15. For personal use only. 2 R. Calderer et al.

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“…Nestes casos, é necessária uma formulação do problema capaz de representar a superfície livre do fluido e, em algumas situações, é interessante também conseguir simular o contato entre as estruturas flutuantes. Essa linha de estudo atrai hoje diversos grupos de pesquisa no mundo [1,2,3,4,5,6,7,8] e em especial no Brasil [9,10,11] em virtude da oportunidade de exploração de petróleo em águas profundas.…”

Section: Introductionunclassified

Método dos elementos finitos com fronteiras imersas aplicado a problemas de dinâmica dos fluidos e interação fluido-estrutura.

Gomes¹

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Residual-based variational multiscale simulation of free surface flows

Cited by 28 publications

References 58 publications

Numerical simulation of particle‐laden flows by the residual‐based variational multiscale method

Numerical simulation of particle‐laden flows by the residual‐based variational multiscale method

Residual-based turbulence models and arbitrary Lagrangian–Eulerian framework for free surface flows

Método dos elementos finitos com fronteiras imersas aplicado a problemas de dinâmica dos fluidos e interação fluido-estrutura.

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