Paper Info
Title
Partitioned Time Stepping for a Parabolic Two Domain Problem
Abstract
There have been many numerical simulations but few analytical results of stability and accuracy of algorithms for computational modeling of fluid-fluid and fluid-structure interaction problems, where two domains corresponding to different fluids (ocean-atmosphere) or a fluid and deformable solid (blood flow) are separated by an interface. As a simplified model of the first examples, this report considers two heat equations in $\Omega_1,\Omega_2\subset\mathbb{R}^2$ adjoined by an interface $I=\Omega_1\cap\Omega_2\subset\mathbb{R}$. The heat equations are coupled by a condition that allows energy to pass back and forth across the interface $I$ while preserving the total global energy of the monolithic, coupled problem. To compute approximate solutions to the above problem only using subdomain solvers, two first-order in time, fully discrete methods are presented. The methods consist of an implicit-explicit approach, in which the action across $I$ is lagged, and a partitioned method based on passing interface values back and forth across $I$. Stability and convergence results are derived for both schemes. Numerical experiments that support the theoretical results are presented.
Year
DOI
Venue
2009
10.1137/080740891
SIAM J. Numerical Analysis
Keywords
Field
DocType
domain problem,approximate solution,numerical experiment,computational modeling,blood flow,fluid-structure interaction problem,heat equation,partitioned time stepping,numerical simulation,total global energy,interface value,analytical result
Convergence (routing),Mathematical optimization,Computer simulation,Mathematical analysis,Heat equation,Discrete time and continuous time,Numerical analysis,Partial differential equation,Mathematics,Numerical stability,Parabola
Journal
Volume
Issue
ISSN
47
5
0036-1429
Citations 
PageRank 
References 
3
0.49
0
Authors
3
Name
Order
Citations
PageRank
Jeffrey M. Connors1263.69
Jason S. Howell2202.32
William J. Layton317072.49