An improved finite element space for discontinuous pressures

Ausas, Roberto F.; Sousa, Fabrício S.; Buscaglia, Gustavo C.

doi:10.1016/j.cma.2009.11.011

Cited by 42 publications

(99 citation statements)

References 24 publications

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“…In this context, the authors found, that applying boundary conditions based on discontinuous shape functions without any additional treatment of the non-conformity may be an effective approach in the solution of physical problems, even though a variational crime is committed. E.g., studies of the authors with a flow solver utilizing discontinuous shape functions as described in [23] show results in agreement with published data from general CFD analysis. This, however, is by no means a general result and different strategies will need to be devised when alternative solvers or formulations are employed.…”

Section: Introductionsupporting

confidence: 79%

A robust algorithm for implicit description of immersed geometries within a background mesh

Baumgärtner

Wolf

Rossi

et al. 2018

Adv. Model. and Simul. in Eng. Sci.

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The paper presents a robust algorithm, which allows to implicitly describe and track immersed geometries within a background mesh. The background mesh is assumed to be unstructured and discretized by tetrahedrons. The contained geometry is assumed to be given as triangulated surface. Within the background mesh, the immersed geometry is described implicitly using a discontinuous distance function based on a level-set approach. This distance function allows to consider both, "double-sided" geometries like membrane or shell structures, and "single-sided" objects for which an enclosed volume is univocally defined. For the second case, the discontinuous distance function is complemented by a continuous signed distance function, whereas ray casting is applied to identify the closed volume regions. Furthermore, adaptive mesh refinement is employed to provide the necessary resolution of the background mesh. The proposed algorithm can handle arbitrarily complicated geometries, possibly containing modeling errors (i.e., gaps, overlaps or a non-unique orientation of surface normals). Another important advantage of the algorithm is the embarrassingly parallel nature of its operations. This characteristic allows for a straightforward parallelization using MPI. All developments were implemented within the open source framework "KratosMultiphysics" and are available under the BSD license. The capabilities of the implementation are demonstrated with various application examples involving practice-oriented geometries. The results finally show, that the algorithm is able to describe most complicated geometries within a background mesh, whereas the approximation quality may be directly controlled by mesh refinement.

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Section: Introductionsupporting

confidence: 79%

A robust algorithm for implicit description of immersed geometries within a background mesh

Baumgärtner

Wolf

Rossi

et al. 2018

Adv. Model. and Simul. in Eng. Sci.

View full text Add to dashboard Cite

show abstract

“…Note that the last integral on the surface ∂Σ = Γ ∩ Σ vanishes if the surface Σ does not intersect the solid boundary or if there is a Dirichlet boundary condition on Γ, in which case the test function v is null. In fact, with an uniform mesh, it has been proved that one may expect at least a O(h 1/2 ) precision in the L 2 -norm [28,23] for the solution of Stokes problem. A better accuracy can be achieved by refining only in the vicinity of interface.…”

Section: Methodsmentioning

confidence: 99%

Direct numerical simulations of two-phase immiscible wakes

Biancofiore¹,

Gallaire²,

Laure³

et al. 2014

Fluid Dyn. Res.

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Abstract. Tammisola et al. [J. Fluid Mech., 713:632-658, 2012] have observed a counter-intuitive destabilizing effect of the surface tension in planar wakes by means of a global linear analysis. In the present study, we conduct direct numerical simulation (DNS) of wakes of two immiscible fluids. The numerical scheme is based on a level set approach to track the interface position. We simulate both sinuous and varicose perturbations of wake flows. DNS confirm a destabilization on the sinuous perturbations in presence of a moderate amount of the surface tension, while wakes are stabilized when the surface tension is further increased. Varicose perturbations present in contrast an intermittent low-amplitude oscillatory regime which does not significantly affect the position of the interface.

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“…Figure 2.8(a) shows the relative difference in friction (|f n − f r |/|f n |), [14,6]. This has been done since the computation of the friction formula (2.26) requires a better treatment of the derivatives at the boundaries.…”

Section: Resultsmentioning

confidence: 99%

“…where 6) and Z 0 , V 0 are the initial position and velocity of the slider resp. assumed to be known.…”

Section: Simulation Details and Untextured Casesmentioning

confidence: 99%

“…[1][2][3][4] That certain textures reduce friction in some hydrodynamic bearings is by no means an obvious phenomenon. Buscaglia et al 5,6 performed asymptotic analyses of general smooth (i.e., untextured) surfaces by introducing short-wavelength periodic perturbations of arbitrary shape and obtained that the untextured shape always (in the hydrodynamic regime) maximizes the load carrying capacity and minimizes the friction coefficient. This implies that, for friction reduction to take place, there exist two possibilities: It can be a consequence of a finite perturbation (outside the validity of asymptotic theory), or involve physical mechanisms which were not considered in the aforementioned mathematical studies, such as cavitation.…”

Section: Introductionmentioning

confidence: 99%

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Modelação matemática de contatos lubrificados micro-texturizados

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An improved finite element space for discontinuous pressures

Cited by 42 publications

References 24 publications

A robust algorithm for implicit description of immersed geometries within a background mesh

A robust algorithm for implicit description of immersed geometries within a background mesh

Direct numerical simulations of two-phase immiscible wakes

Modelação matemática de contatos lubrificados micro-texturizados

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