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Volume 12, Issue 2
A Full Eulerian Fluid-Membrane Coupling Method with a Smoothed Volume-of-Fluid Approach

Satoshi Ii, Xiaobo Gong, Kazuyasu Sugiyama, Jinbiao Wu, Huaxiong Huang & Shu Takagi

Commun. Comput. Phys., 12 (2012), pp. 544-576.

Published online: 2012-12

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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 considered, 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).

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@Article{CiCP-12-544, author = {}, title = {A Full Eulerian Fluid-Membrane Coupling Method with a Smoothed Volume-of-Fluid Approach}, journal = {Communications in Computational Physics}, year = {2012}, volume = {12}, number = {2}, pages = {544--576}, 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 considered, 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).

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.141210.110811s}, url = {http://global-sci.org/intro/article_detail/cicp/7304.html} }
TY - JOUR T1 - A Full Eulerian Fluid-Membrane Coupling Method with a Smoothed Volume-of-Fluid Approach JO - Communications in Computational Physics VL - 2 SP - 544 EP - 576 PY - 2012 DA - 2012/12 SN - 12 DO - http://doi.org/10.4208/cicp.141210.110811s UR - https://global-sci.org/intro/article_detail/cicp/7304.html KW - AB -

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 considered, 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).

Satoshi Ii, Xiaobo Gong, Kazuyasu Sugiyama, Jinbiao Wu, Huaxiong Huang & Shu Takagi. (2020). A Full Eulerian Fluid-Membrane Coupling Method with a Smoothed Volume-of-Fluid Approach. Communications in Computational Physics. 12 (2). 544-576. doi:10.4208/cicp.141210.110811s
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