Introduction to computational methods employed across multiple disciplines to model complex fluid flows on a wide variety of scales. Topics covered include: Review of governing flow and transport equations and their classification; Review of Taylor series and numerical differentiation; Review of interpolation & numerical integration; Numerical solution strategies for ordinary differential equations (ODEs) and elliptic, parabolic, & hyperbolic partial differential equations (PDEs) relevant to fluid flow and transport processes. Finite-difference (FDM), finite-volume (FVM), and finite-element (FEM) methods and computational framework that facilitate parallelization and access to GRID computing resources.

Instructors

Dr Sumanta Acharya
Department of Mechanical Engineering, Louisiana State University

Dr Blaise Bourdin
Department of Mathematics, Louisiana State University

Dr Gabrielle Allen
Department of Computer Science, Louisiana State University
Email: gallen@cct.lsu.edu
Web: http://www.cct.lsu.edu/~gallen
IM: gridrebel
Office hours: Coates Hall: Tuesdays 1pm to 3pm

General Information

Location:
Times: XXXX,Tuesdays and Thursdays

Prerequisites

MATH2070 or MATH2090 or MATH2065+MATH2085 or equivalent; CSC1252 or equivalent

Textbook

Numerical Methods for Partial Differential Equations, William F. Ames, Academic Press, ISBN 0-12-056760-1, RECOMMENDED
Numerical Methods for Engineers, D. V. Griffiths and I. M. Smith, CRC Press, ISBN 0-8493-8610-1 OR
Numerical Analysis, Lee W. Johnson, R. Dean Reiss, Addison Wesley, ISBN 0-201-03442-5
Computational Fluid Dynamics and Heat Transfer, John C. Tannehill, Dale A. Anderson, Richard H. Pletcher, Taylor & Francis, ISBN 1-56032-046-X, REFERENCE

Grading

Undergraduates: Mid-term examination, three projects, homework, final exams

Graduate Students: All requirement for undergraduates except for projects where additional work will be assigned. Cumulative project score weightage will be same as for undergraduates

Score Distribution: 15% HW, 25% Mid-Term Exams; 35% Final Exams; 25% Projects

Other Notes

1. This is an interdisciplinary course from the IGERT program (http://www.cct.lsu.edu/IGERT) on Computational Fluid Dynamics at LSU.

Tentative Schedule

Week	Topic
1	Course Introduction; Review of Governing Equations relevant to fluid flow and transport processes; Classification of equations; Taylor Series
2	Numerical Differentiation ; Order of Accuracy; Finite Differences
3	Numerical Integration; Solution of ODE's (Euler, A-M, A-B, & R-K) for fluid flow and transport; Stability; Stiff Systems
4	Solution of Parabolic Equations for fluid flow and transport (Ut=Uxx); Discretization using Finite-Difference Method (FDM); Boundary Conditions; Accuracy, Stability and Consistency
	Project 1: Parabolic Equation Solver-Assigned
5	Matrix Representation; Direct Solution of System of Equations (TDMA, LU Decomposition); Iterative Solutions (Jacobi, Gauss-Seidel, SOR)
6	Extension to 2D and 3D problems in fluid flow and transport; Solution of System of Equations
7	Elliptic Equation for fluid flow and transport (Uxx=f ); Accuracy and Stability; Solution Strategies;
	Project 1 Due; Mid Term-Exams; Project 2: Elliptic Equation- Assigned
8	Finite-Volume Method (FVM) for elliptic equations
9	Finite-Element Method (FEM) FEM: Discretization; Matrix Assembly
10	FEM: Matrix Assembly; Solution Strategy FEM: Solution Strategy
	Project 2 Due; Project 3: FEM Solver-Assigned
11	First-Order Linear Hyperbolic Equations for fluid flow and transport (U t + cU x = 0); Discretization Strategies;
12	First-Order Non-Linear Hyperbolic Equations for fluid flow and transport (U t + UU x = 0); Discretization; Matrix Linearization;
13	TVD Schemes
14	Parallelization Issues  for flow and transport problems
15	Project 3 Due; Final Exam