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Dr Stephen Millmore (12 hours)


  1. Mesh generation for continuum modelling (Part 1) (Dr N. Gokhale)
    Overview of grid generation techniques; comparison of different mesh types; introduction to cut cell methods; meshing from STL files
  2. Mesh generation for continuum modelling (Part 2) (Dr N. Gokhale)
    Geometric information in cut cell methods; the small cell problem and cut cell approaches; the flux stabilisation cut cell method; convergence properties of cut cell methods
  3. Source terms and equations of state (Part 1)
    Including body forces and other source terms in hyperbolic systems of equations; simple coordinate transformations; derivation of the ideal gas equation of state; mathematical quantities for an equation of state
  4. Equations of state (Part 2) and magnetohydrodynamics (Part 1)
    Equations of state for gases, liquids and solids; reference quantities for defining material properties; tabulated equations of state; modelling a plasma; combining Maxwell’s equations with the Euler equations
  5. Magnetohydrodynamics (Part 2)
    Mathematical properties of the magnetohydrodynamics equations (MHD); numerical methods for MHD; the divergence constraint; from ideal to resistive MHD; MHD for simulating lightning
  6. Elastoplastic solids
    Compressible models for simulating solids; stress, strain and strength; high strain-rate behaviour; evolution equations for an elastoplastic solid; separating elastic and plastic effects


  1. Two-dimensional Euler equations (Part 1)
    Modification of one-dimensional schemes to work in two dimensions, with application to multi-dimensional problems
  2. Two-dimensional Euler equations (Part 2)
    Continuation of the first practical
  3. Geometric source terms
    Allowing one-dimensional codes to run for cylindrical and spherical symmetry, and two-dimensional codes to run in cylindrical symmetry, comparing to results from previous practicals
  4. Beyond the ideal equation of state
    Simulating problems with the stiffened gas equation of state for shocked water, and a Mie-Grüneisen equation of state for a high-speed solid
  5. Magnetohydrodynamics (Part 1)
    Developing a code to solve for one-dimensional MHD problems, with the simulation of multi-wave shock tube tests
  6. Magnetohydrodynamics (Part 2)
    Continuation of the previous practical