This course starts by addressesing classical numerical techniques for partial differential equations. In the end it focuses on modern numerical techniques for partial differential equations from fluid dynamics (the Euler and Navier-Stokes equations). A more detailed, tentative list of topics is given below: Partial differential equations: – types (hyperbolic, parabolic, elliptic), – well-posedness of (initial-) boundary-value problems. Finite-difference methods: – classical methods for the three types, – accuracy analysis, – stability analysis, – iterative solution of linear systems of equations, – test cases and numerical results. Finite-volume methods: – classical methods for convection and diffusion, – monotonicity analysis and limiters, – boundary-condition treatments, – test cases and numerical results. Euler and Navier-Stokes equations: – derivation, – discontinuous solutions, – Riemann solvers, – boundary-condition treatments, – multi-dimensional upwind discretizations, – multigrid methods, – adaptive grid methods, – numerical results.
Two hours per week *Tentaminering *