An accurate, robust, and easy-to-implement method for integration over arbitrary polyhedra: Application to embedded interface methods

Sudhakar, Y.; Almeida, J. P. Moitinho de; Wall, Wolfgang A.

doi:10.1016/j.jcp.2014.05.019

Cited by 64 publications

(55 citation statements)

References 50 publications

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“…This numerical integration is realized with standard Gaussian quadrature rules on all uncut elements in

{scriptT}^{F}

. For the physical fluid domain

{normalΩ}_{{normalΓ}^{F, *}}^{F}

in all intersected elements

{scriptT}_{{normalΓ}^{F, *}}^{F}

, the method described in the work of Sudhakar et al is applied, which utilizes the divergence theorem. For elements that are completely covered by the domain Ω 0 , the fluid weak form does not have to be integrated.…”

Section: Discretization and Solution Approachmentioning

confidence: 99%

A consistent approach for fluid‐structure‐contact interaction based on a porous flow model for rough surface contact

Ager

Schott

Vuong

et al. 2019

Numerical Meth Engineering

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Summary Simulation approaches for fluid‐structure‐contact interaction, especially if requested to be consistent even down to the real contact scenarios, belong to the most challenging and still unsolved problems in computational mechanics. The main challenges are 2‐fold—one is to have a correct physical model for this scenario, and the other is to have a numerical method that is capable of working and being consistent down to a zero gap. Moreover, when analyzing such challenging setups of fluid‐structure interaction, which include contact of submersed solid components, it gets obvious that the influence of surface roughness effects is essential for a physical consistent modeling of such configurations. To capture this system behavior, we present a continuum mechanical model that is able to include the effects of the surface microstructure in a fluid‐structure‐contact interaction framework. An averaged representation for the mixture of fluid and solid on the rough surfaces, which is of major interest for the macroscopic response of such a system, is introduced therein. The inherent coupling of the macroscopic fluid flow and the flow inside the rough surfaces, the stress exchange of all contacting solid bodies involved, and the interaction between fluid and solid are included in the construction of the model. Although the physical model is not restricted to finite element–based methods, a numerical approach with its core based on the cut finite element method, enabling topological changes of the fluid domain to solve the presented model numerically, is introduced. Such a cut finite element method–based approach is able to deal with the numerical challenges mentioned above. Different test cases give a perspective toward the potential capabilities of the presented physical model and numerical approach.

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“…This numerical integration is realized with standard Gaussian quadrature rules on all uncut elements in

{scriptT}^{F}

. For the physical fluid domain

{normalΩ}_{{normalΓ}^{F, *}}^{F}

in all intersected elements

{scriptT}_{{normalΓ}^{F, *}}^{F}

Section: Discretization and Solution Approachmentioning

confidence: 99%

A consistent approach for fluid‐structure‐contact interaction based on a porous flow model for rough surface contact

Ager

Schott

Vuong

et al. 2019

Numerical Meth Engineering

Self Cite

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show abstract

“…Hence, in this work, we allow Γ i to exhibit large deformation, and the crack propagation through the structure introduces a thin opening in the fluid domain ( Figure 3). The recently developed robust numerical integration strategies [30][31][32] are used for the weak form integration. Advanced remeshing strategies are needed to handle these scenarios.…”

Section: The Strongly Coupled Partitioned Approachmentioning

confidence: 99%

A strongly coupled partitioned approach for fluid‐structure‐fracture interaction

Sudhakar

Wall

2018

Numerical Methods in Fluids

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Summary We present a novel method to model large deformation fluid‐structure‐fracture interaction, which is characterized by the fact that the fluid‐induced loads lead to fracture of the structure and the fluid medium fills the resulting crack opening; the mutual interaction between the crack faces and the surrounding fluid contributes substantially to the overall dynamics. A mesh refitting approach is used to model the quasi‐static fracture of the structure, and a robust embedded interface formulation is used to solve the fluid flow equations. The proposed method uses a strongly coupled partitioned scheme with Aitken's Δ2 method as convergence accelerator. Selected numerical examples of increasing complexity are presented to evaluate the performance of the proposed fluid‐structure‐fracture coupling algorithm. The most difficult simulation of the reported examples involves a number of complex phenomena: mixed‐mode crack propagation through the structure, fluid starts to fill the crack opening, complete fracture of the structure into two pieces of which one is carried away by the flow.

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“…It is the use of this quadrature which produces the requirement in Section 3 that the element must contain its own centroid. Clearly, more general integration methods are possible (for example by triangulating the element or using more advanced techniques such as [19,20,24,26]), although for the sake of simplicity this is not something we pursue here. Since each basis function of V E h is defined to be 1 at a single vertex and 0 at the others, we can express…”

Section: The Local Forcing Vectormentioning

confidence: 99%

The virtual element method in 50 lines of MATLAB

Sutton

2016

Numer Algor

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We present a 50-line MATLAB implementation of the lowest order virtual element method for the two-dimensional Poisson problem on general polygonal meshes. The matrix formulation of the method is discussed, along with the structure of the overall algorithm for computing with a virtual element method. The purpose of this software is primarily educational, to demonstrate how the key components of the method can be translated into code.

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An accurate, robust, and easy-to-implement method for integration over arbitrary polyhedra: Application to embedded interface methods

Cited by 64 publications

References 50 publications

A consistent approach for fluid‐structure‐contact interaction based on a porous flow model for rough surface contact

A consistent approach for fluid‐structure‐contact interaction based on a porous flow model for rough surface contact

A strongly coupled partitioned approach for fluid‐structure‐fracture interaction

The virtual element method in 50 lines of MATLAB

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