Computational Hydraulics and Information Management (WSE/HI/04/s)
Prerequisites
Basic Mathematics, Hydraulics, Computational fluid dynamics
Learning objectives
On completion of this module participants should be able to:
- explain the structure of the 1D, 2D and 3D flow equations as representations of conservation laws and know when to use the full dynamic equations and their approximations;
- explain how to model the concentration of substances in the flow;
- classify differential equations in terms of ODE/PDE and determine the nature of a given PDE;
- indicate the nature of the initial and boundary conditions for well posed elliptic, parabolic and hyperbolic problems. Apply the method of characteristics to solve equations;
- implement finite difference schemes to solve ordinary and partial differential equations;
- analyse a numerical scheme and indicate if the scheme is likely to exhibit numerical diffusion, dispersion and/or instability and implement different numerical schemes for water related problems;
- know about the main notions and types of information and knowledge systems and implement information systems using database technology using Delphi application development environment and MS-Access.
Syllabus
Mathematical Formulation of Fluid Flow
Equations (R.K. Price)
Basic concepts; basic physical laws; mass,
momentum and energy fluxes; Eulerian equations; differential forms in common
use; De Saint Venant equations; unsteady flow in pipes; Navier-Stokes equations;
3D Navier-Stokes equations to De Saint Venant equations; advection and
diffusion; dimensional and order of magnitude analyses.
Database, Information and Knowledge Systems
(D.P. Solomatine)
Introduction. Society, information and knowledge.
Data models. Information entities and relations.
Relational data model. Normalisation of tables.
Semantic data model. Main types of
information systems. Distributed and client-server architectures. OLAP,
data warehousing, data mining. Management information systems. Knowledge
bases and expert systems. Knowledge management systems, main notions and
tools.
Development of an information system handling
water usage (exercises and workshops with the use of Delphi and MS-Access).
Numerical Methods I (I. Popescu)
Introduction to differential equations; Differential
equations in fluid dynamics; Initial and boundary value problems; Method
of characteristics; Finite differences for ODE’s; Finite differences for
PDE’s; exercises
Consistency, stability convergence. Fourier
analysis of numerical solutions. Multi-dimensional problems. Diffusion
in 2D.
Didactics
Formal lectures; classroom exercises; home assignments; exercises, workshops in computer lab;
Lecturing materials
- Price: Lecture notes on Mathematical Basis of Computational Hydraulics
- Price: Lecture notes on Mathematical Modelling
- Price: Exercises on Continuum Fluid Dynamics
- Solomatine: Lecture notes on Database, information and knowledge systems
- Popescu: Lecture notes on Numerical methods for Differential Equations
- Books, Presentations