Applied Math Seminar
Monday, October 25, 1999, 4:00pm, 120 Physics
Zhilin Li (North Carolina State University)
The Immersed Interface Method:
A Numerical Approach for Interface Problems
Abstract:- Many physical problems involve interfaces. Examples include phase transition
problems where the interface separates the solid and liquid regions, bubble
simulation, Hele-Shaw flow, composite materials, and many other important
physical phenomena. Mathematically, interface problems usually lead to
differential equations whose input data and solutions have discontinuities
or non-smoothness across interfaces. As a result, many standard numerical
schemes do not work or work poorly for interface problems.
This is an introductory talk about the interface problems and our immersed
interface method. Through some simple examples, I will try to explain the
problems of our interest and related background information. Then I will
present our method for some typical model problems in two dimensions. Our
method can handle both discontinuous coefficients and singular sources.
The main idea is to incorporate the known jumps in the solution and its
derivatives into the finite difference scheme, obtaining a modified scheme
on the uniform grid for quite arbitrary interfaces. The second part of the
talk will focus on applications of the methods combined with the the level
set method for moving interface problems: including the Stokes flow with
different surface tension, the simulation of Hele-Shaw flow, and computation
of crystal growth.
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