Analysis of a One-Dimensional Model for the Immersed Boundary Method

Autor:	Randall J. LeVeque, R. P. Beyer
Rok vydání:	1992
Předmět:	Numerical Analysis Partial differential equation Applied Mathematics Numerical analysis Mathematical analysis Dirac delta function Immersed boundary method Computational Mathematics symbols.namesake Incompressible flow symbols Point (geometry) Heat equation Boundary value problem Mathematics
Zdroj:	SIAM Journal on Numerical Analysis. 29:332-364
ISSN:	1095-7170 0036-1429
DOI:	10.1137/0729022
Popis:	Numerical methods are studied for the one-dimensional heat equation with a singular forcing term, $u_t = u_{xx} + c(t)\delta (x - \alpha (t)).$ The delta function $\delta (x)$ is replaced by a discrete approximation $d_h (x)$ and the resulting equation is solved by a Crank–Nicolson method on a uniform grid. The accuracy of this method is analyzed for various choices of $d_h $. The case where $c(t)$ is specified and also the case where c is determined implicitly by a constraint on the solution at the point a are studied. These problems serve as a model for the immersed boundary method of Peskin for incompressible flow problems in irregular regions. Some insight is gained into the accuracy that can be achieved and the importance of choosing appropriate discrete delta functions.
Databáze:	OpenAIRE
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