To simulate the flow around an object, we can replace the object with the fluid enclosed by a singular force. We can then simulate the flow on a fixed domain with a fluid-fluid interface supporting the singular force. In this paper, we present a boundary condition capturing approach to determine the singular force for a 3D rigid object. We apply a discontinuous body force to enforce the rigid m...

In this paper, we introduce a simple version of immersed interface method (IIM) for the Stokes flow 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 numerical results show that the scheme is second-orde...

In this paper, a hybrid approach which combines the immersed interface method with the level set approach is presented. The fast version of the immersed interface method Li, 1995], is used to solve the diierential equations whose solutions and their derivatives may be discontinuous across the interfaces due to the discontinuity of the coeecients or/and singular sources along the interfaces. The...

Electric field induced particle-particle interactions and assembly are of great interest due to their useful applications in micro devices. The behavior of particles becomes more complex if multiple particles interact with each other at the same time. In this paper, we present a numerical study of two dimensional DC dielectrophoresis based particle-particle interactions and assembly for multipl...

This is the second paper on the study of gradient recovery for elliptic interface problem. In our previous work [H. Guo and X. Yang, 2016, arXiv:1607.05898], we developed a novel gradient recovery technique for finite element method based on body-fitted mesh. In this paper, we propose new gradient recovery methods for two immersed interface finite element methods: symmetric and consistent immer...

The immersed interface method is modified to compute the Schrödinger equation with discontinuous potential. By building the jump condition of the solution into the finite difference approximation near the interface, this method could give at least second order convergence rate for the numerical solution on the uniform cartesian grid. The accuracy of this algorithm is tested via several numerica...

In the immersed interface method, boundaries are represented as singular force in the Navier–Stokes equations, which enters a numerical scheme as jump conditions. Recently, we systematically derived all the necessary spatial and temporal jump conditions for simulating incompressible viscous flows subject to moving boundaries in 3D with second-order spatial and temporal accuracy near the boundar...

An immersed nite element space is used to solve the elliptic interface problems by a nite volume element method. Special nodal basis functions are introduced in a triangle whose interior intersects with the interface so that the jump conditions across the interface are satissed. Optimal error estimates in an energy norm are obtained. Numerical results are supplied to justify the theoretical wor...

Article history: Received 14 January 2011 Received in revised form 31 May 2011 Accepted 8 July 2011 Available online xxxx

Article history: Received 30 May 2012 Received in revised form 2 May 2013 Accepted 19 August 2013 Available online 25 September 2013