scholarly journals The Fast 3D Immersed Interface Method for Poisson Equations on Irregular Domains

2020 ◽  
Vol 10 (3) ◽  
Author(s):  
Elgaddafi Elamami
Keyword(s):  
Irregular Domains ◽  
Immersed Interface Method ◽  
Immersed Interface ◽  
Poisson Equations

An Iterative Two-Fluid Pressure Solver Based on the Immersed Interface Method

2012 ◽  
Vol 12 (2) ◽  
pp. 528-543 ◽  
Author(s):  
Sheng Xu
Keyword(s):  
Fluid Pressure ◽  
Cartesian Grid ◽  
Iteration Step ◽  
Fluid Interfaces ◽  
Order Accuracy ◽  
Immersed Interface Method ◽  
Immersed Interface ◽  
Pressure Poisson Equation ◽  
Poisson Equations ◽  
Two Fluid

AbstractAn iterative solver based on the immersed interface method is proposed to solve the pressure in a two-fluid flow on a Cartesian grid with second-order accuracy in the infinity norm. The iteration is constructed by introducing an unsteady term in the pressure Poisson equation. In each iteration step, a Helmholtz equation is solved on the Cartesian grid using FFT. The combination of the iteration and the immersed interface method enables the solver to handle various jump conditions across two-fluid interfaces. This solver can also be used to solve Poisson equations on irregular domains.

scholarly journals An immersed interface method for the Navier-Stokes equations on irregular domains

PAMM ◽  
2007 ◽  
Vol 7 (1) ◽  
pp. 1025401-1025402
Author(s):  
Zhilin Li ◽  
Ming-Chih Lai ◽  
Kazufumi Ito
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Irregular Domains ◽  
Immersed Interface Method ◽  
Immersed Interface ◽  
Navier Stokes Equations

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

2011 ◽  
Vol 22 (07) ◽  
pp. 687-710 ◽  
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.

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

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.

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