In this paper, a diffuse-interface immersed boundary method (IBM) is proposed to treat three different thermal boundary conditions (Dirichlet, Neumann, Robin) in thermal flow problems. The novel IBM is implemented combining with the lattice Boltzmann method (LBM). The present algorithm enforces the three types of thermal boundary conditions at the boundary points. Concretely speaking, the IBM f...

Submitted for the DFD08 Meeting of The American Physical Society A low-numerical dissipation immersed interface method for the compressible Navier-Stokes equations CARLOS PANTANO, KOSTAS KARAGIOZIS, RAMJI KAMAKOTI, University of Illinois at Urbana-Champaign — Immersed interface methods are an alternative methodology to unstructured methods for solving fluid dynamical problems around complex geo...

The immersed interface method (IIM) by Li and LeVeque has been used successfully for a wide variety of problems. We extended it to nonlinear one-dimensional elliptic and parabolic problems and applied it to traac ow. When applying the IIM to inverse problems in electrical impedance tomography, we found unstabilities that prohibited its use. Recent improvements by Li have overcome the problems (...

In this paper, an immersed finite volume element (IFVE) method is developed for solving some interface problems with nonhomogeneous jump conditions. Using the source removal technique of nonhomogeneous jump conditions, the new IFVE method is the finite volume element method applied to the equivalent interface problems with homogeneous jump conditions and have properties of the usual finite volu...

In this paper, we develop and analyze a trilinear immersed finite element method for solving three-dimensional elliptic interface problems. The proposed can be utilized on interface-unfitted meshes such as Cartesian grids consisting of cuboids. We establish the trace inverse inequalities IFE functions elements with arbitrary interface-cutting configuration. Optimal priori error estimates are ri...

Keywords: Incompressible Stokes equations Singular force Immersed interface method CG-Uzawa method Deformable interface Front tracking Irregular domains Rigid boundaries a b s t r a c t We present an immersed interface method for solving the incompressible steady Stokes equations involving fixed/moving interfaces and rigid boundaries (irregular domains). The fixed/moving interfaces and rigid bo...

Many boundary value problems (BVPs) or initial BVPs have non-smooth solutions, with jumps along lower-dimensional interfaces. The Explicit–Jump Immersed Interface Method (EJIIM) was developed following Li’s Fast Iterative IIM (FIIIM), recognizing that the foundation for the efficient solution of many such problems is a good solver for elliptic BVPs. EJIIM generalizes the class of problems for w...

Contents Preface Introduction xv 1 1.1 A one-dimensional model problem 2 1.2 A two-dimensional example of heat propagation in a heterogeneous material 3 1.3 Examples of irregular domains and free boundary problems 5 1.4 The scope of the monograph and the methodology 5 1.4.1 Jump conditions 7 1.4.2 The choice of grids 7 1.5 A minireview of some popular finite difference methods for interface pro...

The Stokes flow induced by the motion of an elastic massless filament immersed in a two-dimensional fluid is studied. Initially, the filament is deviated from its equilibrium state and the fluid is at rest. The filament will induce fluid motion while returning to its equilibrium state. Two different test cases are examined. In both cases, the motion of a fixed-end massless filament induces the ...

This article describes a trilinear immersed finite element method for solving the EEG forward problem, which is a 3-D elliptic interface problem in the head geometry. The method uses hexahedral Cartesian meshes independent of the interfaces between head tissues, thus avoiding the sometimes difficult task of generating geometry fitting meshes. The interfaces are represented with levelsets and th...