The intrinsic XFEM for two‐fluid flows

Fries, Thomas‐Peter

doi:10.1002/fld.1901

Cited by 63 publications

(63 citation statements)

References 56 publications

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“…It can be seen that due to the viscous damping the amplitude of the height decreases. The mean frequency of the oscillation is 0.277 Hz, which agrees with reported values 0.279 [36] and 0.274 [20]. Note that in this example no difference is observed between the results of the Level Set and PLS methods.…”

Section: Sloshing Tanksupporting

confidence: 90%

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: Sloshing Tanksupporting

confidence: 90%

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 [94], Groß and Reusken present an enriched pressure space in order to avoid spurious discontinuities including surface tension. Fries [84] applied the intrinsic XFEM method to 2D two-fluid flows. Sauerland and Fries [183] compared different enrichment strategies and time-integration schemes over cases with and without surface tension, for two-fluid and free surface flows.…”

Section: Fixed Discretization Methodsmentioning

confidence: 99%

Numerical Modeling and Experimental Validation of Free Surface Flow Problems

Cruchaga

Battaglia

Storti

et al. 2014

Arch Computat Methods Eng

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In this paper we present a summary of numerical methods for solving free surface and two fluid flow problems. We will focus the attention on level set formulations extensively used in the context of the finite element method. In particular, numerical developments to achieve accurate solutions are described. Specific topics of the algorithms, like mass preservation and interface redefinition, are evaluated. To illustrate these aspects, numerical strategies previously developed are applied to the solution of a sloshing and a water column collapse problems. To assess the capabilities of these techniques, the numerical results are compared against each other and with experimental data. Considering these aspects, the present work is aimed to outline some well reported aspects of level set-like formulations.Fil: Cruchaga, Marcela. Universidad de Santiago de Chile; ChileFil: Battaglia, Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones En Metodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones En Metodos Computacionales; ArgentinaFil: Storti, Mario Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones En Metodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones En Metodos Computacionales; ArgentinaFil: D'elia, Jorge. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones En Metodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones En Metodos Computacionales; Argentin

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“…in [7,9,10,13,14,26]. It is mentioned in [23,24] that the space-time elements as discussed in Section 3 are a natural choice in the frame of the XFEM and that time-stepping requires special care.…”

Section: Time Stepping In the Xfemmentioning

confidence: 99%

On time integration in the XFEM

Fries

Zilian

2009

Numerical Meth Engineering

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SUMMARYThe extended finite element method (XFEM) is often used in applications that involve moving interfaces. Examples are the propagation of cracks or the movement of interfaces in two-phase problems. This work focuses on time integration in the XFEM. The performance of the discontinuous Galerkin method in time (space-time finite elements (FEs)) and time-stepping schemes are analyzed by convergence studies for different model problems. It is shown that space-time FE achieve optimal convergence rates. Special care is required for time stepping in the XFEM due to the time dependence of the enrichment functions. In each time step, the enrichment functions have to be evaluated at different time levels. This has important consequences in the quadrature used for the integration of the weak form. A time-stepping scheme that leads to optimal or only slightly sub-optimal convergence rates is systematically constructed in this work.

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The intrinsic XFEM for two‐fluid flows

Cited by 63 publications

References 56 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

Numerical Modeling and Experimental Validation of Free Surface Flow Problems

On time integration in the XFEM

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