4. Scientific Computation
A major component of all the research projects I am involved in is the
development of accurate and efficient numerical methods for systems of
nonlinear (primarily parabolic) PDEs. I work mostly with finite volume
schemes which have been applied in the context of problems in
flow in porous media and
pollutant transport. Some other
examples of related methods I have studied are:

High resolution Godunovtype methods for hyperbolic PDEs:
in which an approximate analytical solution called a
Riemann solver is incorporated into a finite volume scheme
to improve the treatment of discontinuities. I have applied these
methods in the study of a variety of problems, including:

Density from the Euler equations on a moving
grid.

I have made extensive use of
CLAWPACK in this
work, which is a general and robust publiclyavailable code for
solving hyperbolic conservation laws.

Moving mesh methods:
in which the mesh points evolve according to a parabolic moving
mesh PDE that concentrates points in regions where the solution
values or gradients are large. Examples include:
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Last modified: Wed Jul 13 2016
