Scope: The course will provide a solid foundation in the 
mathematics and applications of level-set methods, which 
are used in computational fluid dynamics to capture 
interfaces between distinct materials.

Topics to be covered include:
. Implicit Surface Representation
* Distance Function
* Geometry toolbox (interface normal, curvature, Motion of 
Level Sets)
* Motion due to externally driven velocity field
* Motion in normal direction
* Motion due to Hyperbolic Partial Differential Equations 
(PDEs)
* Linear Advection Equation
* Method of Characteristics
* Conservation Laws
* Hamilton-Jacobi (H-J) Numerical Methods for Hyperbolic 
Conservation Laws & H-J Equations
* Method of Lines
* Upwind schemes
* Lax-Friedrichs schemes
* Monotone Methods, Total Variation Diminishing, 
Essentially Non-Oscillatory 
. Applications of Level Set Methods
* Geodesics
* Simple robotic path planning
* Optimal Control
* Ghost Fluid Method for multi-component compressible fluid 
flow
 

Working Plan: The morning lectures on the theory will be 
complemented by hands-on computational practicals during 
the afternoons. The participants will work on numerical 
exercises as individuals and as members of a team, and 
present their results to the rest of the class.
 
There will also be seminars by established researchers on 
application of CFD to contemporary science and technology 
topics.
 
Who should attend: The course will aim to introduce 
newcomers to level-set methods, their mathematical basis, 
and their applications. It will also provide the foundation 
for existing users who would like to become more involved 
with algorithm and code development. A strong background in 
an applied science or/and mathematics is recommended.
 
At the end of the course the participants will be qualified 
to start building their own code from scratch, or to 
further develop existing packages.