CIEG 684 Syllabus



CIEG 684 Coastal Modeling Methods (3 credits)
Fall 2007

Class: MW 1330-1445, Ocean Engineering Lab 206

Instructors: Jim Kirby
Ocean Engineering Laboratory 201
831-2438
kirby@udel.edu 		Fengyan Shi
Ocean Engineering Laboratory 205
831-2449
fyshi@coastal.udel.edu

Required Text: Morton, K. W. and Mayers, D. F., Numerical Solution of Partial Differential Equations, Cambridge University Press.

Course Schedule (tentative, since this is first time)

Date Main Topic Lecture Topic
8/29 Introduction Why numerical solutions?
9/5 The modern computer environment.
Serial vs. Parallel codes.
Test codes and production codes
9/10 Representing continuum models in discrete form.
Finite differences, finite volumes, finite elements
9/12 Consistency, convergence, stability
9/17 Parabolic equations The heat equation.
Solutions on the infinite line. Solutions in finite domains
9/19 Finite difference approximations (I)
Explicit scheme
Programming a test case in Matlab
9/24 Stability (Fourier and energy methods)
9/26 Finite difference approximations (II)
Implicit schemes. The Crank-Nicolson method. Solution of tri-diagonal matrix equation.
10/1 Example: The one-D vertical boundary layer equation.
10/3 Methods for 2-dimensional spatial domains
10/8 Periodic boundary conditions
10/10 Example: The Parabolic Equation Method for forward-scattering approximations
10/15 Application: The PEM model REF/DIF
10/17 Hyperbolic equations One-way and Two-way Wave equations
Method of Characteristics
10/22 Finite difference approaches (I).
10/24 Finite difference approaches (II). The shock-capturing problem.
10/29 Finite volume methods
10/31 Application: Boussinesq model FUNWAVE
11/5 Elliptic equations Properties of equations
Finite-differences: structure of resulting matrices
Direct and iterative solutions.
11/7 Example: Normal modes of a vibrating plate.
11/12 Finite element method. Weak formulations
11/14 Basis functions. Matrix structure. Solution methods
11/19 Example: Mild Slope Equation
11/21 Application: CGWAVE
11/26 The Boundary Element Method (BEM)
11/28 Navier Stokes equations Equation type?
Solution strategies.
The pressure-Poisson equation
12/3 The split-step method of Chorin, and alternatives
12/5 Application: RIPPLE

Grading: The semester grade will be based on two elements:

Return to CACR home page.

kirby@udel.edu
July 12, 2007