We study convergence of a boundary integral method for 3D interfacial flow with surface tension when the fluid velocity is given by Darcy’s Law. The method is closely related to a previous method developed and implemented by Ambrose, Siegel, and Tlupova, in which one of the main ideas is the use of an isothermal parameterization of the free surface. We prove convergence by proving consistency a...

Maxwell Stress Tensor (MST) method is investigated in this study to quantify the degree of approximation made with the point–dipole method in respect to dielectrophoresis (DEP) in micro–devices. Latex particles and biological cells immersed in aqueous buffers of various conductivities are considered. The two methods (point–dipole and MST full approaches) are compared using analytical dipolar so...

In this paper the Immersed Boundary Method is presented, with some recent developments. The method is used to analyze fluid–structure interaction problems. Different aspects of the method are illustrated by applying it to blood flow in the heart and a flapping filament (flag-in-wind) problem.

The Galerkin finite element method is used to solve the three dimensional continuity, momentum and energy equations for laminar Newtonian and power-law model non-Newtonian flow through horizontal circular tube. The governing equations are non-dimensionalized with respect to specific variables and converted into algebraic equations using appropriate elements. To accelerate convergence a combinat...

In this note we present an immersed boundary (IB) method for restricted diffusion with permeable interfaces. These problems arise under a variety of circumstances, e.g., in thermal contact problems [7]. Diffusion in a medium consisting of two regimes separated by permeable boundaries is another example. It is well-known that cell boundaries in a living tissue are permeable to oxygen and water m...

Yingyi Liu 1,*, Ying Gou 2, Bin Teng 2 and Shigeo Yoshida 1 1 Renewable Energy Center, Research Institute for Applied Mechanics, Kyushu University, Kasuga 8168580, Japan; [email protected] 2 State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China; [email protected] (Y.G.); [email protected] (B.T.) * Correspondence: liuyingyi@r...