Elemental enriched spaces for the treatment of weak and strong discontinuous fields

Idelsohn, Sergio; Giménez, Juan M.; Marti, Julio; Nigro, Norberto M.

doi:10.1016/j.cma.2016.09.048

Cited by 11 publications

(13 citation statements)

References 57 publications

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“…With this approximation, the last integral on the element boundaries of the mass conservation equations becomes null, producing only the last integral on the element boundaries in the momentum equation. These integrals were named interelement forces in the previous work of the authors because they are similar to the introduction of a load on both boundaries of 2 neighboring elements. However, as explained in the aforementioned work, the addition of these integrals must not be understood as the addition of a boundary load.…”

Section: Evaluation Of the Jump Condition For The Internal Interfacesmentioning

confidence: 99%

“…These integrals were named interelement forces in the previous work of the authors because they are similar to the introduction of a load on both boundaries of 2 neighboring elements. However, as explained in the aforementioned work, the addition of these integrals must not be understood as the addition of a boundary load. It must be better interpreted as a do nothing boundary condition between the 2 neighboring elements.…”

Section: Evaluation Of the Jump Condition For The Internal Interfacesmentioning

confidence: 99%

“…For the case of kinks + jumps, the triangle is subdivided in the same way, but the nodes at the internal interface are duplicated. The procedure to obtain the final stiffness matrix of each element to be assembled in the global stiffness matrix may be followed in the previous work of the authors …”

Section: The Finite Element With the Enriched Shape Functionmentioning

confidence: 99%

“…In a previous paper, the authors presented an elemental enriched space capable of reproducing kinks and jumps of the unknown functions using a fixed mesh in which the jumps and kinks do not coincide with the interelement boundaries. In that publication, only thermal problems were solved in which the unknown variable was a scalar function.…”

Section: Introductionmentioning

confidence: 99%

“…A generalization of the treatment of kinks and jumps in the pressure field was presented by Ausas et al However, the enriched space proposed in the aforementioned literature works satisfactorily for the pressure field in the Navier‐Stokes equations but does not work correctly for the enrichment of the temperature field in a typical thermal problem or for the enrichment of the displacement or the velocity field in solid or fluid mechanics problems. As previously stated, Idelsohn et al presented a new elemental enriched space that allows a better approximation of second‐order equations in which an integration by parts is needed. The generalization of these ideas to the incompressible Navier‐Stokes equations is presented next.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Multifluid flows with weak and strong discontinuous interfaces using an elemental enriched space

Idelsohn

Giménez

Nigro

2017

Numerical Methods in Fluids

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In a previous paper the authors present an elemental enriched space to be used in a finite element framework (EFEM) capable to reproduce kinks and jumps in an unknown function using a fixed mesh in which the jumps and kinks do not coincide with the inter-element boundaries. In this previous publication, only scalar transport problems where solved (thermal problems). In the present work these ideas are generalized to vectorial unknowns, in particular the incompressible Navier-Stokes equations for multi-fluid flows presenting internal moving interfaces. The advantage of the EFEM compared with the global enrichment is the important reduction of the computing time when the internal interface is moving. In the EFEM the matrix to be solved at each time-step has, not only the same amount of degrees of freedom (DOFs) but also has always the same connectivity between the DOFs. This frozen matrix-graph improves enormously the efficiency of the solver. Another characteristic of the elemental enriched space presented here is that allows a linear variation of the jump, improving the convergence rate compared with other enriched spaces that have a constant variation of the jump. Furthermore, the implementation in any existing finite element code is extremely easy with the version presented here because the new shape functions are based on the usual FEM shape functions for triangles or tetrahedrals and, once * Corresponding author: Sergio R. Idelsohn; Postal Address; Gran Capitan s/n; Edificio C1, Campus Nord UPC; 08034 Barcelona, Spain; Tel.: +34 93 401 1829; E-mail: sergio@cimne.upc.edu Preprint submitted to Journal Name April 26, 2017 statically condensed the internal DOFs, the resulting elements have exactly the same number of unknowns as the non-enriched finite elements.

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Section: Evaluation Of the Jump Condition For The Internal Interfacesmentioning

confidence: 99%

Section: Evaluation Of the Jump Condition For The Internal Interfacesmentioning

confidence: 99%

Section: The Finite Element With the Enriched Shape Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Multifluid flows with weak and strong discontinuous interfaces using an elemental enriched space

Idelsohn

Giménez

Nigro

2017

Numerical Methods in Fluids

Self Cite

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Computational ElectroHydroDynamics in microsystems: A Review of Challenges and Applications

Narváez-Muñoz,

Hashemi,

Hashemi

et al. 2024

Arch Computat Methods Eng

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Numerical modeling of local capillary effects in porous media as a pressure discontinuity acting on the interface of a transient bi-fluid flow

et al. 2018

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Transient flows through porous media can be controlled by local capillary forces. In an attempt to ease the representation of these complex multiscale flows, this article presents a new numerical approach to account for these local forces, viewed as a global pressure discontinuity acting in bi-fluid flows through smeared-out porous media. A finite element discretization of the Darcy's equations is considered and a pressure enriched space is locally introduced at the fluid interface in order to capture the pressure discontinuity. Then, a Variational Multiscale Stabilization (VMS) method is selected to take into account the subgrid effects on the finite element solution and hence ensure the consistency of the finite element formulation. The fluid front is represented by a level set function, convected with the fluid velocity thanks to a finite element scheme stabilized with a Streamline-Upwind/Petrov-Galerkin (SUPG) method. Both convergence and implementation are first validated with the Method of Manufactured Solution (MMS) and the model shows a good convergence. Second, a comparison with experimental measurements in the case of capillary wicking of water into carbon reinforcements shows a very good correlation between experimental and numerical results.

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Elemental enriched spaces for the treatment of weak and strong discontinuous fields

Cited by 11 publications

References 57 publications

Multifluid flows with weak and strong discontinuous interfaces using an elemental enriched space

Multifluid flows with weak and strong discontinuous interfaces using an elemental enriched space

Computational ElectroHydroDynamics in microsystems: A Review of Challenges and Applications

Numerical modeling of local capillary effects in porous media as a pressure discontinuity acting on the interface of a transient bi-fluid flow

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