A First Course on Level Set Methods
Dr Tariq Aslam (Los Alamos National Laboratory)
Thursday 26th - Friday 27th July 2012
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.