A CutFEM method for two-phase flow problems

Claus, Susanne; Kerfriden, Pierre

doi:10.1016/j.cma.2019.01.009

Cited by 40 publications

(31 citation statements)

References 51 publications

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“…Secondly, we propose an efficient primal-dual numerical algorithm based on the LaTIn algorithm [3,21,22] to solve the 1D/3D coupled problem iteratively. This primal-dual formulation is a natural extension of our previous work on primal-dual CutFEM technologies for unilateral contact problems [12] (see [1,8,19,26] for closely related pieces of work from other research groups), and is relatively new in the context of CutFEM approaches, where consistent penalty formulations are usually chosen as a first step to the development of a coupling strategy [7,11,13]. Finally, CutFEM formulations need to be carefully regularised for system matrices to be well conditioned and, in the context of primal-dual algorithms, for inf-sup stability conditions to be satisfied.…”

Section: Introductionmentioning

confidence: 99%

A mixed-dimensional CutFEM methodology for the simulation of fibre-reinforced composites

Kerfriden

Claus

Mihai

2020

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

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We develop a novel unfitted finite element solver for composite materials with quasi-1D fibrous reinforcements. The method belongs to the class of mixed-dimensional non-conforming finite element solvers. The fibres are treated as 1D structural elements that may intersect the mesh of the embedding structure in an arbitrary manner. No meshing of the unidimensional elements is required. Instead, fibre solution fields are described using the trace of the background mesh. A regularised "cut" finite element formulation is carefully designed to ensure that analyses using such non-conforming finite element descriptions are stable. We also design a dedicated primal/dual operator splitting scheme to resolve the coupling between structure and fibrous reinforcements efficiently. The novel computational strategy is applied to the solution of stiff computational models whereby fibrous reinforcements may lose their bond to the embedding material above a certain level of stress. It is shown that the primal-dual 1D/3D CutFEM scheme is convergent and well-behaved in variety of scenarios involving such highly nonlinear structural computations.

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Section: Introductionmentioning

confidence: 99%

A mixed-dimensional CutFEM methodology for the simulation of fibre-reinforced composites

Kerfriden

Claus

Mihai

2020

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

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“…CutFEM [45][46][47][48][49][50][51] is an extension of XFEM that naturally addresses limit cases associated with complex geometries, and lends itself to image-based simulations. Moreover, we use the libCutFEM library, which is a cut finite element extension of the open-source framework of the FEniCS Project [15][16][17]47].…”

Section: Discretisationmentioning

confidence: 99%

A cut finite element method for spatially resolved energy metabolism models in complex neuro-cell morphologies with minimal remeshing

Farina

Claus²,

Hale

et al. 2021

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

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A thorough understanding of brain metabolism is essential to tackle neurodegenerative diseases. Astrocytes are glial cells which play an important metabolic role by supplying neurons with energy. In addition, astrocytes provide scaffolding and homeostatic functions to neighboring neurons and contribute to the blood–brain barrier. Recent investigations indicate that the complex morphology of astrocytes impacts upon their function and in particular the efficiency with which these cells metabolize nutrients and provide neurons with energy, but a systematic understanding is still elusive. Modelling and simulation represent an effective framework to address this challenge and to deepen our understanding of brain energy metabolism. This requires solving a set of metabolic partial differential equations on complex domains and remains a challenge. In this paper, we propose, test and verify a simple numerical method to solve a simplified model of metabolic pathways in astrocytes. The method can deal with arbitrarily complex cell morphologies and enables the rapid and simple modification of the model equations by users also without a deep knowledge in the numerical methods involved. The results obtained with the new method (CutFEM) are as accurate as the finite element method (FEM) whilst CutFEM disentangles the cell morphology from its discretisation, enabling us to deal with arbitrarily complex morphologies in two and three dimensions.

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“…Application of the finite element method to this system requires the satisfaction of the inf-sup condition to ensure stability of the formulation, 79 often achieved by using different orders of interpolation for the velocity and pressure. In the present work, however, equal order interpolations are preferred and stability is ensured using a continuous interior penalty method following the approach of Burman et al 79 (see also Claus and Kerfriden, 80 ).…”

Section: Discrete Crack Flowmentioning

confidence: 99%

The simulation of transport processes in cementitious materials with embedded healing systems

Freeman

Jefferson

2019

Num Anal Meth Geomechanics

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A new model for simulating the transport of healing agents in self-healing (SH) cementitious materials is presented. The model is applicable to autonomic SH material systems in which embedded channels, or vascular networks, are used to supply healing agents to damaged zones. The essential numerical components of the model are a crack flow model, based on the Navier-Stokes equations, which is coupled to the mass balance equation for simulating unsaturated matrix flow. The driving forces for the crack flow are the capillary meniscus force and the force derived from an external (or internal) pressure applied to the liquid healing agent. The crack flow model component applies to non-uniform cracks and allows for the dynamic variation of the meniscus contact angle, as well as accounting for inertial terms. Particular attention is paid to the effects of curing on the flow characteristics. In this regard, a kinetic reaction model is presented for simulating the curing of the healing agent and a set of relationships established for representing the variation of rheological properties with the degree of cure. Data obtained in a linked experimental programme of work is employed to justif the hoi e a d fo of the o stituti e elatio ships, as ell as to ali ate the odel s evolution functions. Finally, a series of validation examples are presented that include the analysis of a series of concrete beam specimens with an embedded vascular network. These examples demonstrate the ability of the model to capture the transport behaviour of this type of SH cementitious material system.

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A CutFEM method for two-phase flow problems

Cited by 40 publications

References 51 publications

A mixed-dimensional CutFEM methodology for the simulation of fibre-reinforced composites

A mixed-dimensional CutFEM methodology for the simulation of fibre-reinforced composites

A cut finite element method for spatially resolved energy metabolism models in complex neuro-cell morphologies with minimal remeshing

The simulation of transport processes in cementitious materials with embedded healing systems

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