Curriculum::Courses::Introductory, Cross-Disciplinary Courses
XD II: Course Outline
Course Title: |
"Multi-Scale Fluid Dynamics: Computational Methods" |
Course Number: |
ME7953-3, X-listed in MATH, PHYS, BIO, CSC |
Prerequisites: |
MATH2070 or MATH2090 or MATH2065+MATH2085 or equivalent; CSC1252 or equivalent |
Text(s) & Readings: |
TBA |
Description |
An introduction to computational methods that are employed across multiple disciplines to model complex fluid flows on a wide variety of scales. Topics to be covered include: Interpolation; numerical integration & differentiation; solution of ordinary differential equations (ODEs) and partial differential equations (PDEs). Techniques for solving PDEs of elliptic, parabolic, & hyperbolic form will be introduced with fluid-flow examples. Finite-difference (FDM), finite-volume (FVM), and finite-element (FEM) methods will be introduced along with computational frameworks that facilitate parallelization and access to GRID computing resources. Throughout this course, example exercises will focus on the numerical solution of a set of governing mathematical equations that is common to fluid flow problems in a wide variety of physical and biological settings. The origin of these equations and the physical concepts that underpin them are discussed in a companion course, XD-I. |
Schedule |
Week |
Topic | Instructor |
|
1 |
Course Introduction; Numerical Interpolation Taylor Series |
Acharya |
|
2 |
Numerical Integration & Differentiation; Finite Differences Order of Accuracy |
Acharya |
|
3 |
Solution of ODE's (Euler, A-M, A-B, & R-K); Stability; Stiff Systems |
Allen |
|
4 |
Solution of Elliptic Equations (U xx = f); Discretization using Finite-Difference Method (FDM); Boundary Conditions; Accuracy, Stability and Consistency |
Acharya |
|
5 |
Matrix Representation; Direct Solution of System of Equations (TDMA, LU Decomposition); Iterative Solutions (Jacobi, Gauss-Seidel, SOR) |
Acharya |
|
6 |
Extension to 2D and 3D; Solution of System of Equations |
Acharya |
|
7 |
Extension to Unsteady Elliptic Equation (U t = a U xx ); Accuracy and Stability; Solution Strategies; Boundary Conditions (including Cyclic Conditions); |
Acharya |
|
8 |
Finite-Volume Method (FVM), Finite-Element Method (FEM) and their Relationship to FDM; FVM:
|
Bourdin |
|
9 |
FEM:
|
Bourdin |
|
10 |
First-Order Linear Hyperbolic Equations (U t + cU x = 0); Discretization Strategies; Numerical Properties (Stability, Accuracy and Consistency) |
White |
|
11 |
First-Order Non-Linear Hyperbolic Equations (U t + UU x = 0); Discretization; Matrix Linearization; TVD Schemes |
White |
|
12 |
Burger's Equation (U t + cU x = cU xx ); Discretization Schemes |
White |
|
13 |
Parallelization and Framework Issues | Allen |
|
14 |
Survey Lectures on Multi-Grid, Pre-Conditioning, etc. | Acharya |
News
07/13/2005:-
LSU one of only
20 institutions to
recieve a $3M
program award
from National
Science Foundation
Funding to support
unique, multi-
disciplinary training
of doctoral students.
Read More...
Events
No Upcoming Events
IGERT Brochure
IGERT Office
Center for Computation & Technology
Johnston Hall
Louisiana State University
Baton Rouge, LA - 70803
