1. The mathematical model in Hydraulic Engineering. Numerical solution of hydraulic algebraic equations.
2. One-dimensional motion of bodies in a fluid, initial value problems.
3. Ordinary/partial differential equations. Basic methods of numerical analysis, (Euler method, Runge-Kutta method, numerical solutions of equations).
4. Methods of discretising equations. Taylor expansion. Discretisation for first and second-order derivatives. Composite forms of discretisation of equations. Analysis of discretisation error of equations.
5. Stability and consistency of a numerical scheme. Von Neumann method. Finite difference method. Solving illustrative problems using the finite difference method.
6. Solving problems of parabolic partial differential equations (PDEs). Forward difference methods (FTCS), Crank–Nicolson. Finite difference method in multidimensional problems. Indicative problems: Rayleigh problem, Boundary layer flow.
7. Solving elliptic PDE problems. Liebmann, Richardson, SOR schemes. Solving the Poisson equation. Indicative problems: Dynamic flow in a non-rectangular duct. Dynamic flow around a cylinder.
8. Solving problems of hyperbolic PDEs. Upwind methods, upstream, Lax, Leapfrog, non-expressed Euler. Higher-order upwind numerical schemes. Indicative problems: Wave propagation, Shock wave formation.
9. Use of open-source software and/or commercial software.

Learning Outcomes

The course material includes the basic knowledge in the field of computational hydraulics. The course includes computational simulations in one-dimensional and two-dimensional flows and applications to basic hydraulic problems with computational methodologies and hydraulic analysis software.

Upon successful completion of the course, the student will be able to:

• It recognises the operation of iterative numerical schemes and the basic concepts, such as the consistency and convergence of a numerical scheme.
• It analyses hydraulic engineering problems and solves them by combining numerical models and basic knowledge of numerical analysis.
• It combines basic numerical methods and develops elementary algorithms to solve the problem.
• It simulates complex problems using open-source and/or commercial software.
• It depicts numerical solutions to fundamental fluid mechanics problems.