A Full Eulerian Fluid-Membrane Coupling Method with a Smoothed Volume-of-Fluid Approach (Communications in Computational Physics, 2020)
A novel full Eulerian fluid-elastic membrane coupling method on the fixedCartesian coordinate mesh is proposed within the framework of the volume-of-fluidapproach. 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 bulkstructure 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 generallycalled VOF function. A smoothed indicator (or characteristic) function is introducedas a phase indicator which results in a smoothed VOF function. This smoothed VOFfunction uses a smoothed delta function, and it enables a membrane singular force tobe 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-Hookeanand the Skalak models are employed in the numerical simulations. A smoothed (andless dissipative) interface capturing method is employed for the advection of the VOFfunction and the quantities defined on the membrane. The stability restriction due tomembrane stiffness is relaxed by using a quasi-implicit approach. The present methodis validated by using the spherical membrane deformation problems, and is applied toa pressure-driven flow with the biconcave membrane capsules (red blood cells).