CENTER FOR COMPUTATIONAL MATHEMATICS COLLOQUIUM

                  UNIVERSITY OF COLORADO AT DENVER



TITLE:   Numerical Solutions of Partial Differential 
         Equations on Unbounded Domains
 

SPEAKER: Houde Han, Department of Applied Mathematics, Tsinghua University
         Beijing,  P. R. of China
         
DATE:    Monday, December 8, 1997  


PLACE:   Mathematics Conference Room 626 
         UCD Building, 1250 14th St., Denver


TIME:    noon (Refreshments served at 11:45 am) 



ABSTRACT

Many boundary value problems of partial differential equations involving
the unbounded domain arise in practical applications, such as fluid flow 
around obstacle, the coupling of structure with foundation and environment.
In finding the numerical solutions of partial differential equations on 
unbounded domain, one difficulty is the unboundedness of the physical 
domain, hence the finite element method and the finite difference method
can not be used directly. In engineering, the usual method is to introduce
a bounded computational domain by an artificial boundary. For example, 
Neumann boundary condition or Dirichlet boundary condition is often used on
the given artificial boundary. In general, the above boundary conditions 
are only very rough approximations of the exact boundary condition at the 
artificial boundary.

During the last ten years the methods to design the artificial boundary 
conditions with high accuracy on a given artificial boundary or solving 
partial differential equations on an unbounded domain numerically have 
been studied often. In this talk we will introduce some new development on 
this subject. Specially we are interested in the steady viscous 
incompressible fluid flow around abody in a flat channel. We designed a 
discrete artificial boundary condition for the linear N-S equations in 
stream-function, vorticity formulation and applied it to numerical 
simulations of steady  viscous incompressible fluid flow in a channel.