Immersed finite element method

Zhang, Lucy; Gerstenberger, Axel; Wang, Xiaodong; Liu, Wing Kam

doi:10.1016/j.cma.2003.12.044

Cited by 460 publications

(394 citation statements)

References 17 publications

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“…In this paper, we employ a direct numerical simulation (DNS) based on arbitrary Lagrangian-Eulerian (ALE) FEM (Refs. [22][23][24][25] to accurately resolve the complicated fluid-particle interfacial motions. Both translational and rotational motions of a nanoparticle in a (i) stationary fluid medium and (ii) Poiseuille flow are investigated.…”

Section: Introductionmentioning

confidence: 99%

Nanoparticle Brownian motion and hydrodynamic interactions in the presence of flow fields

et al. 2011

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We consider the Brownian motion of a nanoparticle in an incompressible Newtonian fluid medium (quiescent or fully developed Poiseuille flow) with the fluctuating hydrodynamics approach. The formalism considers situations where both the Brownian motion and the hydrodynamic interactions are important. The flow results have been modified to account for compressibility effects. Different nanoparticle sizes and nearly neutrally buoyant particle densities are also considered. Tracked particles are initially located at various distances from the bounding wall to delineate wall effects. The results for thermal equilibrium are validated by comparing the predictions for the temperatures of the particle with those obtained from the equipartition theorem. The nature of the hydrodynamic interactions is verified by comparing the velocity autocorrelation functions and mean square displacements with analytical and experimental results where available. The equipartition theorem for a Brownian particle in Poiseuille flow is verified for a range of low Reynolds numbers. Numerical predictions of wall interactions with the particle in terms of particle diffusivities are consistent with results, where available.

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Section: Introductionmentioning

confidence: 99%

Nanoparticle Brownian motion and hydrodynamic interactions in the presence of flow fields

et al. 2011

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“…The IMFEM [78][79][80][81][82][83] is a computational framework to concurrently deal with the relevant physical interactions in biological environments [80,84,85], including fluid-structure interaction (FSI) [82,86,87], cell-cell interaction [81,88,89], thermal fluctuation [78,79,90], electrokinetics [83,91,92], self-assembly behaviour [79,[93][94][95] and other mesoscale and molecular effects [96]. In this work, the IMFEM will be used to simulate the blood flow as well as the microcirculation of NPs.…”

Section: Model and Methodologymentioning

confidence: 99%

Cell and nanoparticle transport in tumour microvasculature: the role of size, shape and surface functionality of nanoparticles

et al. 2016

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Through nanomedicine, game-changing methods are emerging to deliver drug molecules directly to diseased areas. One of the most promising of these is the targeted delivery of drugs and imaging agents via drug carrier-based platforms. Such drug delivery systems can now be synthesized from a wide range of different materials, made in a number of different shapes, and coated with an array of different organic molecules, including ligands. If optimized, these systems can enhance the efficacy and specificity of delivery compared with those of non-targeted systems. Emerging integrated multiscale experiments, models and simulations have opened the door for endless medical applications. Current bottlenecks in design of the drug-carrying particles are the lack of knowledge about the dispersion of these particles in the microvasculature and of their subsequent internalization by diseased cells (Bao et al . 2014 J. R. Soc. Interface 11 , 20140301 ( doi:10.1098/rsif.2014.0301 )). We describe multiscale modelling techniques that study how drug carriers disperse within the microvasculature. The immersed molecular finite-element method is adopted to simulate whole blood including blood plasma, red blood cells and nanoparticles. With a novel dissipative particle dynamics method, the beginning stages of receptor-driven endocytosis of nanoparticles can be understood in detail. Using this multiscale modelling method, we elucidate how the size, shape and surface functionality of nanoparticles will affect their dispersion in the microvasculature and subsequent internalization by targeted cells.

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“…The approach used in this work is in some ways related to other methods for dealing with complex boundaries, such as the Immersed Boundary Method (IBM), Immerse Finite Element Method (IFEM) [37], and the Finite cell method (FCM) [24]. IBM and IFEM are widely used in fluid mechanics.…”

Section: Introductionmentioning

confidence: 99%

Volumetric parametrization from a level set boundary representation with PHT-splines

Chan

Anitescu

Rabczuk

2017

Computer-Aided Design

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A challenge in isogeometric analysis is constructing analysis-suitable volumetric meshes which can accurately represent the geometry of a given physical domain. In this paper, we propose a method to derive a splinebased representation of a domain of interest from voxel-based data. We show an efficient way to obtain a boundary representation of the domain by a level-set function. Then, we use the geometric information from the boundary (the normal vectors and curvature) to construct a matching C 1 representation with hierarchical cubic splines. The approximation is done by a single template and linear transformations (scaling, translations and rotations) without the need for solving an optimization problem. We illustrate our method with several examples in two and three dimensions, and show good performance on some standard benchmark test problems.

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Immersed finite element method

Cited by 460 publications

References 17 publications

Nanoparticle Brownian motion and hydrodynamic interactions in the presence of flow fields

Nanoparticle Brownian motion and hydrodynamic interactions in the presence of flow fields

Cell and nanoparticle transport in tumour microvasculature: the role of size, shape and surface functionality of nanoparticles

Volumetric parametrization from a level set boundary representation with PHT-splines

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