Short introduction with a review of other numerical methods or the basic equations of fluid dynamics. Conservation laws: the Navier-Stokes equations.
Different levels of approximation, the Euler and boundary-layer equations. Basics of finite approximations for partial differential equations.
Mathematical properties of hyperbolic systems. Numerical treatment of shocks. Finite difference and volume methods. Boundary conditions. High-resolution methods. Coordinate transformation and grid-quality assessment. Practical algorithms for compressible and incompressible flow. Computer exercises with methods for the Euler equations in 1D and different approximations for 2D compressible and incompressible flows.