The stable XFEM for two-phase flows

Sauerland, Henning; Fries, Thomas‐Peter

doi:10.1016/j.compfluid.2012.10.017

Cited by 86 publications

(82 citation statements)

References 35 publications

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“…The enrichment shape functions with small support typically occur when the interface is close to a node or edge and lead to an ill-conditioned system matrix. Two approaches to treat this problem are given in [30][31][32]. In this work we use the blocking criteria proposed in [30] in which for each cut element enrichment is considered if the ratio between the minimum and maximum sub-volumes is bounded by a userdefined constant C 1, i.e.…”

Section: Enrichmentmentioning

confidence: 99%

A locally extended finite element method for the simulation of multi-fluid flows using the Particle Level Set method

Kamran

Rossi

Oñate

2015

Computer Methods in Applied Mechanics and Engineering

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The simulation of immiscible two-phase flows on Eulerian meshes requires the use of special techniques to guarantee a sharp definition of the evolving fluid interface. This work describes the combination of two distinct technologies with the goal of improving the accuracy of the target simulations. First of all, a spatial enrichment is employed to improve the approximation properties of the Eulerian mesh. This is done by injecting into the solution space new features to make it able to correctly resolve the solution in the vicinity of the moving interface. Then, the Lagrangian Particle Level Set (PLS) method is employed to keep trace of the evolving solution and to improve the mass conservation properties of the resulting method. While the local enrichment can be understood in the general context of the XFEM, we employ an element-local variant, which allows preserving the matrix graph, and hence highly improving the computational efficiency.

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Section: Enrichmentmentioning

confidence: 99%

A locally extended finite element method for the simulation of multi-fluid flows using the Particle Level Set method

Kamran

Rossi

Oñate

2015

Computer Methods in Applied Mechanics and Engineering

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“…In order to treat the discontinuity of the pressure due to the presence of the surface tension the extended finite element method (XFEM) is applied, see e.g. [7].…”

Section: Numerical Approximationmentioning

confidence: 99%

“…[11]. A modification of the standard finite element method is used in order to properly address the arising spurious currents nearby the free surface caused by the discontinuous pressure, see [7] or [5]. The implemented method is verified by solution of a benchmark problem, cf.…”

Section: Introductionmentioning

confidence: 99%

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On numerical approximation of incompresible fluid flow with free surface influenced by surface tension

Sváček

2017

EPJ Web Conf.

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Abstract. This paper deals with the numerical approximation of two immiscible incompressible fluids flow. The two-dimensional problem is mathematically described with the aid of the incompressible Navier-Stokes equations. The motion of the two phases is treated with the aid of level set method. The surface tension effects are taken into account as well as the contact angle influence. The problem is formulated in a weak sense and discretized with the aid of the finite element method. The details of the numerical methods are given and several possibilities of the realization of the surface tension term are discussed. Numerical results are shown.

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“…[17] or [15]. In the case of high surface tension, a modification of the standard FE method is required to avoid the spurious currents, see [16] or [3]. For the verification of the implemented method a benchmark problem is solved, cf.…”

Section: Introductionmentioning

confidence: 99%

On Numerical Approximation of Two-Phase Flow With Surface Tension and Contact Angles With Level Set Approach

Sváček¹,

Pokorný²

2018

Topical Problems of Fluid Mechanics 2018

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In this paper the problem of flow of two immiscible incompressible fluids is considered, mathematically modelled and numerically approximated. The surface tension and the static contact angle effects are considered, its mathematical realization is discussed and applicable numerical procedures are described. The finite element method is used for approximation, the extended finite element method is used to treat the pressure discontinuity caused by the surface tension. The numerical results are shown.

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The stable XFEM for two-phase flows

Cited by 86 publications

References 35 publications

A locally extended finite element method for the simulation of multi-fluid flows using the Particle Level Set method

A locally extended finite element method for the simulation of multi-fluid flows using the Particle Level Set method

On numerical approximation of incompresible fluid flow with free surface influenced by surface tension

On Numerical Approximation of Two-Phase Flow With Surface Tension and Contact Angles With Level Set Approach

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