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...

Article history: Received 12 September 2016 Received in revised form 7 February 2017 Accepted 8 February 2017 Available online 14 February 2017

We investigate the dynamics of a flexible, elastic fibre, suspended in a fluid and subjected to a 3D shear flow. Simulations are performed using the “Immersed Boundary Method,” and are distinguished by their ability to capture the hydrodynamic interaction between the fluid and fibre, as well as the detailed structure of the individual fibres. Suspensions of flexible fibres are encountered in ma...

The immersed boundary method is both a mathematical formulation and a numerical scheme for problems involving the interaction of a viscous incompressible fluid and a (visco-)elastic structure. In [M.-C. Lai, Simulations of the flow past an array of circular cylinders as a test of the immersed boundary method, Ph.D. thesis, Courant Institute of Mathematical Sciences, New York University, 1998; M...

This paper presents an implementation of the second-order accurate immersed interface method to simulate the motion of the flexible elastic membrane immersed in two viscous incompressible fluids with different viscosities, which further develops the work reported in Tan et al. [Z.-J. Tan, D.V. Le, K.M. Lim, B.C. Khoo, An Immersed Interface Method for the Incompressible Navier–Stokes Equations w...