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A Full Eulerian Fluid-Membrane Coupling Method with a Smoothed Volume-of-Fluid Approach

Published online by Cambridge University Press:  20 August 2015

Satoshi Ii ,
Xiaobo Gong ,
Kazuyasu Sugiyama ,
Jinbiao Wu ,
Huaxiong Huang  and
Shu Takagi
Satoshi Ii*
Affiliation:
Department of Mechanical Engineering, The University of Tokyo, 7-3-1 Hongo Bunkyo-ku, Tokyo, 113-8656, Japan
Xiaobo Gong*
Affiliation:
Department of Engineering Mechanics, NAOCE, Shanghai Jiaotong University, Shanghai 200240, China
Kazuyasu Sugiyama*
Affiliation:
Department of Mechanical Engineering, The University of Tokyo, 7-3-1 Hongo Bunkyo-ku, Tokyo, 113-8656, Japan
Jinbiao Wu*
Affiliation:
LMAM & School of Mathematical Sciences, Peking University, Beijing 100871, China
Huaxiong Huang*
Affiliation:
Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario, Canada
Shu Takagi*
Affiliation:
Department of Mechanical Engineering, The University of Tokyo, 7-3-1 Hongo Bunkyo-ku, Tokyo, 113-8656, Japan Computational Science Research Program, RIKEN, 2-1 Hirosawa Wako, Saitama, 351-0198, Japan
*
Corresponding author.Email:sii@fel.t.u-tokyo.ac.jp
Email:x.gong@sjtu.edu.en
Email:sugiyama@fel.t.u-tokyo.ac.jp
Email:jwu@math.pku.edu.cn
Email:hhuang@yorku.ca
Email:takagi@mech.t.u-tokyo.ac.jp
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Abstract

A novel full Eulerian fluid-elastic membrane coupling method on the fixed Cartesian coordinate mesh is proposed within the framework of the volume-of-fluid approach. The present method is based on a full Eulerian fluid-(bulk) structure coupling solver (Sugiyama et al., J. Comput. Phys., 230 (2011) 596-627), with the bulk structure replaced by elastic membranes. In this study, a closed membrane is consid-ered, and it is described by a volume-of-fluid or volume-fraction information generally called VOF function. A smoothed indicator (or characteristic) function is introduced as a phase indicator which results in a smoothed VOF function. This smoothed VOF function uses a smoothed delta function, and it enables a membrane singular force to be incorporated into a mixture momentum equation. In order to deal with a membrane deformation on the Eulerian mesh, a deformation tensor is introduced and updated within a compactly supported region near the interface. Both the neo-Hookean and the Skalak models are employed in the numerical simulations. A smoothed (and less dissipative) interface capturing method is employed for the advection of the VOF function and the quantities defined on the membrane. The stability restriction due to membrane stiffness is relaxed by using a quasi-implicit approach. The present method is validated by using the spherical membrane deformation problems, and is applied to a pressure-driven flow with the biconcave membrane capsules (red blood cells).

Keywords

74F1076M2074L15Fluid-membrane interactionEulerian formulationCartesian meshvolume-of-fluidquasi-implicit approachred blood cell

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 12 , Issue 2 , August 2012 , pp. 544 - 576
Copyright
Copyright © Global Science Press Limited 2012

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