Introduction
This course introduces the principles and fundamentals of numerical methods in hydraulics. It covers techniques for solving various hydraulic problems using numerical methods such as finite difference, finite volume, and finite element methods. The official syllabus of this course in persian can be downloaded here.
Key Topics
Part 1: Theoretical Foundations of Numerical Methods
- Necessity and applications of numerical methods in problem solving
- Understanding numerical modeling including various stages:
- Defining the problem and governing equations
- Discretizing the governing equations
- Applying initial and boundary conditions
- Calibration and evaluation of results
- Classification of differential equations:
- Elliptic equations (e.g., Poisson's equation)
- Parabolic equations (e.g., diffusion equation)
- Hyperbolic equations (e.g., transport equation)
- Introduction and comparison of various numerical methods:
- Finite difference
- Finite volume
- Finite element method
- Numerical solution of differential equations:
- Elliptic equations:
- Discretization methods
- Introducing Jacobi algorithm, Gauss-Seidel algorithm and ...
- Implying boundary conditions
- Parabolic equations:
- Implicit methods
- Explicit methods
- Crank-Nicholson methods
- Alternating Direction Implicit (ADI) methods
- Hyperbolic equations:
- Temporal and spacial discretization
- Implication of boundary conditions
- Criteria for evaluating numerical methods:
- Stability, accuracy, consistency, and convergence
Part 2: Applications of Numerical Methods in Practical Computations
- Numerical modeling of flows:
- One-dimensional steady flow in channels and rivers
- One-dimensional unsteady flow in channels and rivers using Saint-venant equation
- Two-dimensional steady flow in channels and rivers using steady shallow water equations
- Two-dimensional unsteady flow in channels and rivers using shallow water equations (SWE)
- Solving the advection-diffusion equation in natural environments:
- Modeling environmental phenomena (e.g., pollutant transport in water)
- Numerical solution of water hammer and hydraulic transients:
- Pressure analysis in pressurized pipelines
- Numerical solution of flow in porous media:
- Applications in modeling groundwater flow
Teaching Methods
The course utilizes lectures with slides, interactive Q&A sessions, and problem-solving exercises. Practical examples and real-world applications are included to enhance understanding.
Evaluation
- Continuous assessment: 25%
- Final exam (written): 50%
- Project work: 25%
Resources
- Computational Hydraulics by M.B. Abbot and A.W. Minns, 1994
- Open-Channel Flow by M.H. Chaudhry, 1993
- Applied Hydraulic Transients by M.H. Chaudhry, 1987
- Practical Aspects of Computational River Hydraulics by J.A. Cunge, F.M. Holly Jr., and A. Verwey, 1980
- River Mechanics by P.Y. Julien, 2002
- Computational Hydraulics - An Introduction by C.B. Vreugdenhil, 1989
- Numerical Solution of Partial Differential Equations: Finite Difference Methods by G.D. Smith, 1985
- Computational Hydraulics: Numerical Methods and Modelling by I. Popescu, 2014
- Computational Methods for Fluid Dynamics by Joel H. Ferziger, Milovan Perić, and Robert L. Street, 2019
Additional Considerations
The course can be delivered in a hybrid format (online and in-person) with content tailored for virtual or in-person sessions. Standard university facilities and computational tools are sufficient for effective delivery.