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Dr Nikos Nikiforakis (12 hours)

a) Governing equations for gases and fluids

  1. Conservation laws for mass, momentum and energy – integral and PDE form
  2. Introduction to compressible and incompressible forms
  3. Simple equations of state - ideal and stiffened `gases'
  4. Riemann problems
  5. Introduction to cylindrical and spherical symmetry and source terms (geometric, gravity)

b) Governing equations for elastic solids

c) Governing equations for magnetohydrodynamics

  1. Combining Maxwell's equations with the Euler equations
  2. Need for divergence cleansing, and implementation strategies

d) Discretisation approaches for continuum equations

e) Finite difference vs. finite volume

f) First order Godunov method and the Riemann problem

g) Higher order methods, slope limited (MUSCL), `weighted' (ENO, WENO)