Lecture Note on Fundamentals of Computational Hydraulics
Preface:
Any physical system is a three-dimensional system and can be consist of very simple processes to complex processes. In-order to understand and predict its nature and behavior, we want to study that physical system. Studying of any system can be done on its actual system, scale model, or mathematical model. A scale model is a small scale prototype of a physical system, and a mathematical model is a mathematical representation of a physical system. A mathematical model can be consist of simple to complex mathematical equations with linear and/or non-linear terms, and ordinary or partial differential equation terms. In most of the cases, direct/analytical solution of these mathematical equations is not possible. Therefore, numerical methods come into an action.
In any numerical methods, mathematical equations are solved in discrete form using different numerical schemes. In this course, fundamentals of Mathematical modeling will be covered. First we will learn the nature of different differential equations and their analytical solutions. Then, we will learn a basic numerical method, i.e., Finite Difference Method (FDM) and use that method to solve different differential equations. Later on different special modeling applications, e.g., modeling unsteady flow, modeling water quality process, modeling sediment transport, modeling ground water flow, and modeling hydrological processes will be covered in this course. Knowledge on basic numerical methods, especially, solutions of non-linear equations and solutions of system of linear/non-linear equations, is a pre-requisite for this course. Moreover, having knowledge on any programming language will be advantageous.
Table of Contents:
Chapter 1: Introduction to Mathematical Modeling
Chapter 2: Review of Numerical Methods
Chapter 3: Review of Programming Language - MATLAB
Chapter 4: Analytical Solution of Differential Equations
Chapter 5: Numerical Solution of Differential Equations
Chapter 6: Modeling Advection-Diffusion Processes
Chapter 7: Modeling Unsteady Flow
Chapter 8: Modeling Ground Water Flow