Introduction to Computational Multiphysics [M12] (E)

Dr. Stephen Millmore (12 hours)

Lectures:

1. Introduction to computational multiphysics
   Definition of multiphysics problems; representation of material interfaces; the challenges of multiphysics modelling; overview of multiphysics methods
2. Level set methods
   Implicit boundary methods and an introduction to the uses of level set methods; mathematical properties of level set methods applied to interfaces; numerical methods for the level set function; reinitialisation techniques
3. Ghost fluid methods (Part 1)
   Dynamic boundary conditions; derivation of the original ghost fluid method; techniques to improve the ghost fluid method; numerical requirements for implementing a ghost fluid method
4. Diffuse interface methods
   Mixture quantities for a diffuse interface; the Baer-Nunziato system of equations for diffuse interfaces; velocity and pressure equilibrium limits; speed of sound in a mixture; numerical methods for diffuse interface approaches
5. Ghost fluid methods (Part 2)
   Improving accuracy through Riemann problem-based ghost fluid methods; mixed material Riemann problems; interfaces between very different materials; ghost fluid methods in multiple dimensions;
6. Cavitation and surface tension
   Cavitation from liquids in tension; a diffuse interface approach to cavitation; surface forces in a discretised domain; a sharp interface approach to surface tension

Practicals:

1. Mixed-material exact Riemann solvers
   Expanding the exact Riemann solver developed at the end of CCM1 to allow for two materials either side of the interface.  Preparatory work for later practicals
2. Level set methods
   Incorporating a level set method into existing Euler equation codes as a passive scalar.  Demonstrating that this can track a contact discontinuity
3. The original ghost fluid method
   Incorporating a true material interface between two ideal gases, using level set methods and the original ghost fluid method of Fedkiw et al.
4. The original ghost fluid method for multiple interfaces
   Increasing the applicability of the ghost fluid method code such that it can deal with the complex case of a multi-interface simulation
5. The Riemann ghost fluid method
   Implementing a Riemann problem-based ghost fluid method, and using this to solve scenarios the basic method could not cope with
6. Surface tension
   Implementing the techniques to deal with surface tension in a toy one-dimensional problem