Finite element procedures for computing normals and mean curvature on triangulated surfaces and their use for mesh refinement

Cenanovic, Mirza; Hansbo, Peter; Larson, Mats G.

doi:10.48550/arxiv.1703.05745

Cited by 2 publications

(2 citation statements)

References 26 publications

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“…For triangulated surfaces, one approach is to adopt alternative basis functions, such as those used by subdivision surfaces [110], which provide enough regularity to yield accurate pointwise approximations to curvature and surface derivatives by directly differentiating the shape functions. Another approach is to use methods of discrete differential geometry using averaging Voronoi cells [111] or finite element stabilization techniques [112]. In the immersogeometric FSI methodology [113], higher order spline-based surface representation can be used, following the original work on isogeometric analysis [114].…”

Section: Discussionmentioning

confidence: 99%

An immersed interface method for discrete surfaces

Kolahdouz

Bhalla

Craven

et al. 2020

Journal of Computational Physics

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Fluid-structure systems occur in a range of scientific and engineering applications. The immersed boundary (IB) method is a widely recognized and effective modeling paradigm for simulating fluidstructure interaction (FSI) in such systems, but a difficulty of the IB formulation of these problems is that the pressure and viscous stress are generally discontinuous at fluid-solid interfaces. The conventional IB method regularizes these discontinuities, which typically yields low-order accuracy at these interfaces. The immersed interface method (IIM) is an IB-like approach to FSI that sharply imposes stress jump conditions, enabling higher-order accuracy, but prior applications of the IIM have been largely restricted to numerical methods that rely on smooth representations of the interface geometry. This paper introduces an immersed interface formulation that uses only a C 0 representation of the immersed interface, such as those provided by standard nodal Lagrangian finite element methods. Verification examples for models with prescribed interface motion demonstrate that the method sharply resolves stress discontinuities along immersed boundaries while avoiding the need for analytic information about the interface geometry. Our results also demonstrate that only the lowest-order jump conditions for the pressure and velocity gradient are required to realize global second-order accuracy. Specifically, we demonstrate second-order global convergence rates along with nearly second-order local convergence in the Eulerian velocity field, and between first-and second-order global convergence rates along with approximately first-order local convergence for the Eulerian pressure field. We also demonstrate approximately second-order local convergence in the interfacial displacement and velocity along with first-order local convergence in the fluid traction along the interface. As a demonstration of the method's ability to tackle more complex geometries, the present approach is also used to simulate flow in a patient-averaged anatomical model of the inferior vena cava, which is the large vein that carries deoxygenated blood from the lower extremities back to the heart. Comparisons of the general hemodynamics and wall shear stress obtained by the present IIM and a body-fitted discretization approach show that the present method yields results that are in good agreement with those obtained by the body-fitted approach.

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Section: Discussionmentioning

confidence: 99%

An immersed interface method for discrete surfaces

Kolahdouz

Bhalla

Craven

et al. 2020

Journal of Computational Physics

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“…We will now replace the mean curvature vector H = κn Γ with a smoothened discrete curvature [24,23,10], H h , as detailed in the following. Let [H n h ] d denote the vector-valued continuous piecewise linear finite element space over the domain formed by the band of all intersected elements at time t = t n .…”

Section: Stabilised Scheme For the Surface Tension Forcementioning

confidence: 99%

A CutFEM method for two-phase flow problems

Claus

Kerfriden

2019

Computer Methods in Applied Mechanics and Engineering

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In this article, we present a cut finite element method for two-phase Navier-Stokes flows. The main feature of the method is the formulation of a unified continuous interior penalty stabilisation approach for, on the one hand, stabilising advection and the pressure-velocity coupling and, on the other hand, stabilising the cut region. The accuracy of the algorithm is enhanced by the development of extended fictitious domains to guarantee a well defined velocity from previous time steps in the current geometry. Finally, the robustness of the moving-interface algorithm is further improved by the introduction of a curvature smoothing technique that reduces spurious velocities. The algorithm is shown to perform remarkably well for low capillary number flows, and is a first step towards flexible and robust CutFEM algorithms for the simulation of microfluidic devices.

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Finite element procedures for computing normals and mean curvature on triangulated surfaces and their use for mesh refinement

Cited by 2 publications

References 26 publications

An immersed interface method for discrete surfaces

An immersed interface method for discrete surfaces

A CutFEM method for two-phase flow problems

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