On the Jump Conditions for an Immersed Interface Method

AbstractIn this paper, an immersed interface method is presented to simulate the dynamics of inextensible interfaces in an incompressible flow. The tension is introduced as an augmented variable to satisfy the constraint of interface inextensibility and the resulting augmented system is solved by the GMRES method. In this work, the arclength of the interface is locally and globally conserved as the enclosed region undergoes deformation. The forces at the interface are calculated from the configuration of the interface and the computed augmented variable, and then applied to the fluid through the related jump conditions. The governing equations are discretized on a MAC grid via a second-order finite difference scheme which incorporates jump contributions and solved by the conjugate gradient Uzawa-type method. The proposed method is applied to several examples including the deformation of a liquid capsule with inextensible interfaces in a shear flow. Numerical results reveal that both the area enclosed by interface and arclength of interface are conserved well simultaneously. These provide further evidence on the capability of the present method to simulate incompressible flows involving inextensible interfaces.

Download Full-text

ANALYSIS OF OPTICAL WAVEGUIDES WITH ARBITRARY INDEX PROFILE USING AN IMMERSED INTERFACE METHOD

International Journal of Modern Physics C ◽

10.1142/s0129183111016543 ◽

2011 ◽

Vol 22 (07) ◽

pp. 687-710 ◽

Cited By ~ 4

Author(s):

THEODOROS P. HORIKIS

Keyword(s):

Optical Waveguides ◽

Eigenvalue Problems ◽

Numerical Technique ◽

Interface Problems ◽

Index Profile ◽

Immersed Interface Method ◽

Immersed Interface ◽

Light Confinement ◽

Bragg Fibers ◽

Matrix Eigenvalue Problems

A numerical technique is described that can efficiently compute solutions of interface problems. These are problems with data, such as the coefficients of differential equations, discontinuous or even singular across one or more interfaces. A prime example of these problems are optical waveguides, and as such the scheme is applied to Maxwell's equations as they are formulated to describe light confinement in Bragg fibers. It is based on standard finite differences appropriately modified to take into account all possible discontinuities across the waveguide's interfaces due to the change of the refractive index. Second- and fourth-order schemes are described with additional adaptations to handle matrix eigenvalue problems, demanding geometries and defects.

Download Full-text

MATHEMATICAL MODELLING AND COMPUTER SIMULATION OF TEMPERATURE DISTRIBUTION IN INHOMOGENEOUS COMPOSITE SYSTEMS WITH IMPERFECT INTERFACE

Engineering Structures and Technologies ◽

10.3846/2029882x.2014.972643 ◽

2014 ◽

Vol 6 (2) ◽

pp. 77-85

Author(s):

Pratibha Joshi ◽

Manoj Kumar

Keyword(s):

Numerical Simulation ◽

Heat Flux ◽

Temperature Distribution ◽

Imperfect Interface ◽

Immersed Interface Method ◽

Immersed Interface ◽

Composite Systems ◽

Steady State Temperature ◽

Perfect Interface ◽

Inhomogeneous Composite

Many studies have been done previously on temperature distribution in inhomogeneous composite systems with perfect interface, having no discontinuities along it. In this paper we have determined steady state temperature distribution in two inhomogeneous composite systems with imperfect interface, having discontinuities in temperature and heat flux using decomposed immersed interface method and performed the numerical simulation on MATLAB.

Download Full-text