SUMMARY Many physical problems involve interior interfaces across which the coeecients in the problem, the solution, its derivatives, the ux, or the source term may have jumps. These interior interfaces may or may not align with a underlying Cartesian grid. Zhilin Li, in his dissertation, showed how to discretize such elliptic problems using only a Cartesian grid and the known jump conditions t...

In this paper we consider a modiication of the immersed boundary method based on a nite element approximation of the uid. Besides some theoretical considerations, we present two dimensional numerical examples which connrm the good behavior of the computed solutions.

Article history: Received 16 November 2010 Received in revised form 15 February 2011 Accepted 9 March 2011 Available online 16 March 2011

Article history: Received 7 April 2016 Received in revised form 10 November 2016 Accepted 25 November 2016 Available online 29 November 2016

In this paper a simulation model is presented for the Direct Numerical simulation (DNS) of multiphase flow. This method combines the Volume of fluid model and Immersed Boundary method in order to investigate water-oil flow-pattern. The simulations were carried out on structured cartesian adaptive mesh refinement (SAMR), where the the Immersed Boundary represents the circular tube via Direct For...

In this paper, finite difference schemes based on asymptotic analysis and the augmented immersed interface method are proposed for potential problems with an inclusion whose characteristic width is much smaller than the characteristic length in one and two dimensions. We call such a problem as a crack problem for simplicity. In the proposed methods, we use asymptotic analysis to approximate the...

In this paper, we introduce a simple version of the immersed interface method (IIM) for Stokes flows with singular forces along an interface. The numerical method is based on applying the Taylor’s expansions along the normal direction and incorporating the solution and its normal derivative jumps into the finite difference approximations. The fluid variables are solved in a staggered grid, and ...

The Immersed Interface Method is employed to solve the time-varying electric field equations around a three-dimensional vesicle. To achieve second-order accuracy the implicit jump conditions for the electric potential, up to the second normal derivative, are derived. The trans-membrane potential is determined implicitly as part of the algorithm. The method is compared to an analytic solution ba...

The flow behavior of many multiphase flow applications is greatly influenced by wetting properties and the presence of surfactants. We present a numerical method for two-phase flow with insoluble surfactants and contact line dynamics in two dimensions. The method is based on decomposing the interface between two fluids into segments, which are explicitly represented on a local Eulerian grid. It...

Abstract A model problem in electrical impedance tomography for the identification of unknown shapes from data in a narrow strip along the boundary of the domain is investigated. The representation of the shape of the boundary and its evolution during an iterative reconstruction process is achieved by the level set method. The shape derivatives of this problem involve the normal derivative of t...