An immersed interface method for discrete surfaces

An Immersed Interface Method for Incompressible Navier-Stokes Equations

An immersed interface method for the vortex - in - cell algorithm †

The paper presents a two-dimensional immersed interface technique for the vortex-in-cell (VIC) method for the simulation of flows past complex geometries. The particle–mesh VIC algorithm is augmented by a local particle– particle (PP) correction term in a particle–particle particle–mesh (PPPM) context to resolve sub-grid scales incurred by the presence of the immersed interface. The PP correcti...

Optimal convergence analysis of an immersed interface finite element method

We analyze an immersed interface finite element method based on linear polynomials on noninterface triangular elements and piecewise linear polynomials on interface triangular elements. The flux jump condition is weakly enforced on the smooth interface. Optimal error estimates are derived in the broken H1-norm and L2-norm.

A Rothe-immersed Interface Method for an Elliptic-parabolic Interface Problem

INTRODUCTION This paper concerns what we term a parabolic-elliptic interface problem. Two – dimensional problems are investigated in many papers [1-4]. They arise in the study of two-dimensional eddy currents [2], in the quasistationary two-dimensional magnetic fields [1], surface measurements [3], etc. In the present paper we shall concentrate on the following simplified model from the biochem...

An Immersed Interface Method for the Incompressible Navier--Stokes Equations with Discontinuous Viscosity Across the Interface

We present an immersed interface method for solving the incompressible Navier– Stokes equations with discontinuous viscosity across the interface and singular forces. The method is based on the augmented strategy proposed by Li, Ito, and Lai [Comput. Fluids, 36 (2007), pp. 622–635] to decouple the jump conditions of the fluid variables through the introduction of two augmented variables. In the...