Immersed electrokinetic finite element method yaling liu department of mechanical engineering, northwestern university, 2145 sheridan road, evanston, il 60208. Fully variational formulation of immersed finite element method using comsol as a finite element library. Theory, implementation, and practice november 9, 2010 springer. In order to maintain the noslip condition and the divergencefree property simultaneously, an iterative scheme of immersed boundary method in the finite element framework is presented. On computational issues of immersed finite element methods. Furthermore, ifem is combined with electrokinetics to study the mechanisms of nanobio filament assembly for the understanding of cell motility. Immersed electrokinetic finite element method nasaads.
An immersed finite element method with integral equation correction thomas ruberg and fehmi cirak. The alcf is committed to providing training and outreach opportunities that prepare researchers to efficiently use its leadership computing systems, while also cultivating a diverse and skilled hpc workforce for the future. A cylindrical storage tank of diameter d contains a liquid at depth or head hx,t. In ifem, a lagrangian solid mesh moves on top of a background eulerian fluid mesh which spans over the entire computational domain.
In computational fluid dynamics, the immersed boundary method originally referred to an approach developed by charles peskin in 1972 to simulate fluidstructure fiber interactions. An electric field induced concentration has been studied for such purposes but with limited success due to limited efficacy. Use the principle of conservation of mass to arrive at the governing equation of the. The proposed immersed molecular electrokinetic finite element method couples electrokinetics with fluctuating hydrodynamics to study the motion and deformation of flexible objects immersed in a. Boundary value problems are also called field problems. A new method is proposed for modelling the electrokinetic induced mechanical motion of particles in a fluid domain under an applied electric field. Treating the coupling of the structure deformations and the fluid flow poses a number of challenging problems for numerical simulations the elastic boundary changes the flow of the fluid and the fluid moves the. Immersed electrokinetic finite element method liu, yaling. Oa20180175 october 2019 an immersed finite element method for elliptic. Cut nite element immersed boundary method derivation of the algorithm energy stability. Datta s, ghosal s, patankar na, electroosmotic flow in a rectangular channel with variable. The immersed interface method iim 6,7,911 is an efficient finite difference approach for interface. A highorder eulerianlagrangian finite element method for. An immersed finite element method based on a locally.
T1 nanoscale sensor analysis using the immersed molecular electrokinetic finite element method. Fully variational implementation of immersed finite element method for fluidstructure interaction applications nitesh nama, tony jun huang, and francesco costanzo department of engineering science and mechanics the pennsylvania state university, state college, pa, usa namahuangcostanzo immersed finite element methodimmersed finite element. Solving interface problems of the helmholtz equation by. The immersed interface method using a finite element formulation. The approach taken is mathematical in nature with a strong focus on the. Fully variational implementation of immersed finite element. Kyle dunn wpi a cutfem ibm crrel ron liston seminar 7 30. N2 the concentration and detection of molecular biomarkers remain as a challenge to develop pointofcare diagnostic devices. Introduction finite element discretization of domains with complex, timedependent geometric features pose challenges in terms. It encourages the development of finite element automatic mesh generation algorithms prevalence of methods. Chung, immersed electrokinetic finite element method, international journ.
An immersed finite element method with integral equation. Above the start of the finite element method as described period, the final form was created using tens or hundreds of design elements for many users it. Modeling of soft tissues interacting with fluid blood or. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach. An immersed finite element method for elliptic interface.
Design and optimization of a nanotip sensor via immersed molecular electrokinetic finite element method. With finite element formulations for both fluid and solid domains, the submerged structure is solved more. The proposed immersed molecular electrokinetic finite element method couples electrokinetics with fluctuating hydrodynamics to study the motion and deformation of flexible objects immersed in a suspending medium under an applied electric field. A 3d immersed finite element method with nonhomogeneous. Asme 2010 first global congress on nanoengineering for medicine and biology. Immersed electrokinetic finite element method liu 2007. This method is able to eliminate the aforementioned drawbacks of the ib method by adopting parts of the work on the extended immersed boundary method eibm. Modeling of soft tissues interacting with fluid blood or air. However, our framework described here can be used for high order immersed interface.
Mixed immersed finite element for stokes interface problems 3 figure 2. Above the start of the finite element method as described period, the final form was created using tens or hundreds of design elements for many users it was enough to be very simple simulations of simulated. The concentration and detection of molecular biomarkers remain as a challenge to develop pointofcare diagnostic devices. Apr 15, 2008 ib methods use the finite difference scheme, while the ifem employs two kinds of finite element meshes. Immersed finite element method for rigid body motions in the. Dielectrophoretic effect of nonuniform electric fields on. An immersed finite element method with integral equation correction. In this article, we develop a taylorhood immersed nite element ife method to solve twodimensional stokes interface problems. A possible solution consists in enriching the finite element basis on the elements that are crossed by the immersed boundary, such that the irregularity of the solution is taken into account. The problem can be solved by both finite difference methods and finite element methods.
The immersed interface method using a finite element. The latest stable version of the full source code is available at. An example of methods using local enrichments are the socalled extended finite element method xfem see 1. Pdf applications of finite element method with examples. International journal for numerical methods in engineering, 861. A p2p1 partially penalized immersed finite element method for stokes interface problems yuan chen and xu zhang abstract. Nanoscale sensor analysis using the immersed molecular.
A highorder eulerianlagrangian finite element method for coupled electromechanical systems by gerd brandstetter a dissertation submitted in partial satisfaction of the requirements for the degree of doctor of philosophy in engineering mechanical engineering in the graduate division of the university of california, berkeley committee in. An immersed finite element method for planar elasticity. Immersed interface method iim which is a modified finite difference method is used to solve the governing 2d elliptic electrostatic equations with irregular boundaries. Immersed finite element method for rigid body motions in. A 3d immersed finite element method with nonhomogeneous interface flux jump for applications in particleincell simulations of plasmalunar surface. The immersed continuum method and its applications. Design and optimization of a nanotip sensor via immersed. Advantages of ifem single velocity field ensures continuity of velocity across the interface automatically. The finite element method fem, or finite element analysis fea, is a computational technique used to obtain approximate solutions of boundary value problems in engineering. The immersed boundary ib method was introduced to model blood flow through.
Finite element methods such as those mentioned above can be applied to solve interface problems provided that they use a body. In this paper, the immersed finite element method ifem is proposed for the solution of complex fluid and deformable structure interaction problems encountered in many physical models. In this method, the characteristicbased split scheme is employed to solve the momentum equations and the formulation for the pressure and the extra body force. A neutral particle polarizes under the application of an electric field and causes local nonuniformity in electrostatic potential distribution. Request pdf immersed electrokinetic finite element method a new method is proposed for modelling the electrokinetic induced mechanical motion of particles in a fluid domain under an applied. A t hree dimensional immersed smoothed finite element. A method of lines based on immersed finite elements for. The key idea of the ife method is to mesh the domain independently of the interface location and allow elements to be.
A 3d immersed finite element method with nonhomogeneous interface flux jump for applications in particleincell simulations of plasmalunar surface interactions. A unique simulation technique has been developed capable of modeling electric field induced detection of biomolecules such as viruses. Pdf immersed electrokinetic finite element method semantic. A fully coupled immersed finite element method for fluid. The field is the domain of interest and most often represents a physical structure. A divergencefree immersed boundary method and its finite. We remark that immersed nite element or nite di erence methods have been extensively studied in the literature. Immersed finite element method and its applications to biological. Therefore, the fluid mesh is of eulerian type while the structure mesh can be viewed as lagrangian description in conjunction with the socalled flow map.
Immersed molecular electrokinetic finite element method. Zienkiewicz,cbe,frs unesco professor of numerical methods in engineering international centre for numerical methods in engineering,barcelona previously director of the institute for numerical methods in engineering university ofwales,swansea r. Immersed finite element method northwestern scholars. Basedon the ife method, the immersed finite element particleincell. International journal for numerical methods in engineering.
Proceedings of the asme 2010 first global congress on nanoengineering for medicine and biology. Based on structured cartesian meshes, we develop a three. An immersed finite element method and its application to. Immersed finite element method for interface problems with algebraic multigrid solver by wenqiang feng a thesis presented to the faculty of the graduate school of missouri university of science and technology in partial ful. Fully variational implementation of immersed finite. Partially penalized immersed finite element methods for. In the initial attempt to employ finite element formulations with immersed methods, socalled ex tended immersed boundary method was introduced to represent. Method for elliptic interface problems, proceedings of the international conference on. Immersed finite element method and its applications to. For a full discussion of existing immersed finite element methods see 1929 and the references therein. International journal for numerical methods in engineering 2007. Farrell et al, immersed finite element method and applications to biological systems, computer methods in applied mechanics and engineering, 19517221749, 2006.
Immersed finite element method for interface problems with. This paper presents a computational study for investigating t. In our approach, the fluid domain is modeled using an eulerian formulation with the finite element method similarly as ifem, however, we use a meshfree particle method the efgm to model the solid domain. Immersedboundary methods for general finitedifference and finite. Feb 15, 2006 recently, following the pioneering work of peskin and coworkers on the ib method, an alternative approach, the immersed finite element method ifem was developed by zhang et al. Alternatively, based on the immersed type methods a class of methods using fixed fluid grid or mesh have been proposed, such as the immersed boundary ib methods 18, immersed finite element method ifem 1923, 2d immersed smoothed finite element methods 2d isfem 24, 25 and so on. Introduction to finite element analysis fea or finite. Mittal and iaccarino 2 refer to all these and other related methods as immersed boundary methods and provide various categorizations of these methods. The field is the domain of interest and most often represents a. Immersed electrokinetic finite element method 381 here, the immersed.
The immersed interface method for elliptic equations with. May 28, 2004 in the proposed immersed finite element method ifem, we will eliminate the aforementioned drawbacks of the ib method and adopt parts of the work on the extended immersed boundary method eibm recently developed by wang and liu. Hybrid immersed interfaceimmersed boundary methods for ac. The immersed fictitious element method for fluidstructure interaction.
Department of engineering, university of cambridge, uk summary we propose a robust immersed. Immersed particle method for fluidstructure interaction university of. Multiscale framework for biomedical simulation from molecular. A continuum mechanicsbased musculomechanical model for. Jul 01, 2018 the immersed boundary method cut nite element method cutfem 3. Abstract a new method is proposed for modelling the electrokinetic. The immersed finite element method20,21 is developed by merging the concept of immersed boundary,2224 finite element, and meshfree25,26 methods for nonlinear fluids and. Immersed electrokinetic finite element method request pdf. These include methods such as the immersed interface method, the cartesian grid method, the ghost fluid method and the cutcell method. The immersed molecular electrokinetic finite element method imefem framework used in our study is an extension of our previous verified and validated. In the nite di erence setting, we refer to the immersed boundary method in 28, the immersed interface method in 22, 24, the ghost uid method in 27, and the references therein. The method presented here uses immersed finite element ife functions for the discretization in spatial variables that can be carried out over a fixed mesh such as a cartesian mesh if desired, and this feature makes it possible to reduce the parabolic equation to a system of ordinary differential equations ode through the usual semi. Liu y, liu wk, belytschko t, patankar na, to ac, kopacz a, chung jh, immersed electrokinetic finite element method, international journal for numerical methods in engineering 71 4. An unconditionally stable cut finite element immersed.
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