The Finite Element Immersed Boundary Method for the Numerical Simulation of the Motion of Red Blood Cells in Microfluidic Flows

2013 ◽  
pp. 3-17 ◽  
Author(s):  
Ronald H. W. Hoppe ◽  
Christopher Linsenmann
Keyword(s):  
Numerical Simulation ◽  
Finite Element ◽  
Red Blood Cells ◽  
Immersed Boundary Method ◽  
Blood Cells ◽  
Immersed Boundary ◽  
Boundary Method ◽  
Microfluidic Flows

Direct Simulation of Dense Suspensions of Non-Spherical Particles

2011 ◽  
Author(s):  
Orest Shardt ◽  
Jos Derksen
Keyword(s):  
Reynolds Number ◽  
Red Blood Cells ◽  
Sedimentation Rate ◽  
Immersed Boundary Method ◽  
Blood Cells ◽  
Volume Fraction ◽  
Immersed Boundary ◽  
Direct Simulation ◽  
Rigid Particles ◽  
Boundary Method

We describe the direct simulation of high-solids-fraction suspensions of non-spherical rigid particles that are slightly denser than the fluid. The lattice-Boltzmann method is used to solve the flow of the interstitial Newtonian fluid, and the immersed boundary method is used to enforce a no-slip boundary condition at the surface of each particle. The surface points for the immersed boundary method are also employed for collision handling by applying repulsive forces between nearby surface points. Due to the finite number of these points, the method simulates rough surface collisions. We also discuss methods for integrating the equations of particle motion at low density ratios and propose a method with improved accuracy. Rigid particles shaped like red blood cells were simulated. Simulations of a single particle showed that the particle settles in its original orientation when the Reynolds number is low (1.2) but flips to a higher drag orientation when the Reynolds number is higher (7.3). A simulation with a 45% solids volume fraction and a low solid over fluid density ratio showed the possibility of simulating blood as it is found in the body. A simulation at a lower solids volume fraction (35%) was used to compare the results with the erythrocyte sedimentation rate (ESR), a common blood test. The sedimentation rate was estimated as 0.2 mm/hr, which is an order of magnitude lower than a typical ESR of about 6 mm/hr for a healthy adult. The most likely reasons for the discrepancy are the omission of agglomeration-inducing inter-cellular forces from the simulations and the treatment of the red blood cells as rigid particles.

THE TECHNIQUE OF THE IMMERSED BOUNDARY METHOD: APPLICATIONS TO THE NUMERICAL SOLUTIONS OF IMCOMPRESSIBLE FLOWS AND WAVE SCATTERING

2009 ◽  
Vol 23 (03) ◽  
pp. 437-440 ◽  
Author(s):  
HONGQUAN CHEN ◽  
LING RAO
Keyword(s):  
Numerical Simulation ◽  
Finite Element ◽  
Immersed Boundary Method ◽  
Fictitious Domain ◽  
Immersed Boundary ◽  
Fictitious Domain Method ◽  
Lagrangian Multipliers ◽  
Element Discretization ◽  
Domain Method ◽  
Boundary Method

A fictitious domain method, in which the Dirichlet boundary conditions are treated using boundary supported Lagrangian multipliers, is considered. The technique of the immersed boundary method is incorporated into the framework of the fictitious domain method. Contrary to conventional methods, it does not make use of the finite element discretization. It has a simpler structure and is easily programmable. The numerical simulation of two-dimensional incompressible inviscid uniform flows over a circular cylinder validates the methodology and the numerical procedure. The numerical simulation of propagation phenomena for time harmonic electromagnetic waves by methods combining controllability and fictitious domain techniques is also presented. Using distributed Lagrangian multipliers, the propagation of the wave can be simulated on an obstacle free computational region with regular finite element meshes essentially independent of the geometry of the obstacle and by a controllability formulation which leads to algorithms with good convergence properties for time-periodic solutions. The numerical results presented are in good agreement with those in the literature using obstacle fitted meshes.

FINITE ELEMENT APPROACH TO IMMERSED BOUNDARY METHOD WITH DIFFERENT FLUID AND SOLID DENSITIES

2011 ◽  
Vol 21 (12) ◽  
pp. 2523-2550 ◽  
Author(s):  
DANIELE BOFFI ◽  
NICOLA CAVALLINI ◽  
LUCIA GASTALDI
Keyword(s):  
Finite Element ◽  
Immersed Boundary Method ◽  
Stokes Equations ◽  
Numerical Procedure ◽  
Biological Tissues ◽  
Immersed Boundary ◽  
Fluid Structure ◽  
Finite Element Approach ◽  
Boundary Method ◽  
Element Approach

The Immersed Boundary Method (IBM) has been designed by Peskin for the modeling and the numerical approximation of fluid-structure interaction problems, where flexible structures are immersed in a fluid. In this approach, the Navier–Stokes equations are considered everywhere and the presence of the structure is taken into account by means of a source term which depends on the unknown position of the structure. These equations are coupled with the condition that the structure moves at the same velocity of the underlying fluid. Recently, a finite element version of the IBM has been developed, which offers interesting features for both the analysis of the problem under consideration and the robustness and flexibility of the numerical scheme. Initially, we considered structure and fluid with the same density, as it often happens when dealing with biological tissues. Here we study the case of a structure which can have a density higher than that of the fluid. The higher density of the structure is taken into account as an excess of Lagrangian mass located along the structure, and can be dealt with in a variational way in the finite element approach. The numerical procedure to compute the solution is based on a semi-implicit scheme. In fluid-structure simulations, nonimplicit schemes often produce instabilities when the density of the structure is close to that of the fluid. This is not the case for the IBM approach. In fact, we show that the scheme enjoys the same stability properties as in the case of equal densities.

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