Time Schedule:
Uri Shumlak
A A 543
Seattle Campus
Numerical approximation of the inviscid compressible equations of fluid dynamics. Analysis of numerical accuracy, stability, and efficiency. Use of explicit, implicit, and flux split methods. Discussion of splitting, approximate factorization, discrete point, and finite volume approaches. Applications to the solution of simple hyperbolic systems of equations and the Euler equations. Offered: W.
Class description
AA 543 is an introductory, graduate-level course in computational fluid dynamics. The student will be exposed to the following topics:
* Introduction to CFD, Applications, Current Computer Architectures
* Governing Equations & Assumptions, Equation Types, Model Equations, Potential Flow, Heat Conduction, Wave Eqn, Burger’s Eqn, Euler Eqns
* Panel Methods, Finite Differences, Algorithms, Errors and Accuracy, Consistency Stability and Convergence, Finite Volumes, Explicit Algorithms, Implicit Algorithms, Numerical Boundary Conditions, Method of Lines, Shock Jump Relations, Shock Capturing, Elliptic Methods for Subsonic Potential Flow, Relaxation Algorithms
* 1-D Euler Eqns, Lax-Wendroff Scheme, MacCormack Scheme, Implicit q-method, Pseudo 1-D Euler Eqns, Boundary Conditions, Flux-Splitting, Artificial Viscosity, Flux Limiters
* Multi-Dimensional Euler Eqns, Lax-Wendroff and MacCormack Schemes, Stability of Multi-Dimensional Schemes, Operator Splitting, Implicit Algorithms, Beam Warming Algorithm, Approximate Factorization, Other Algorithms
* Generalized Coordinates, Coordinate Transformations, Boundary Conditions in Generalized Coordinates, Introduction to Grid Generation
Student learning goals
Students will learn the fundamental concepts of computational fluid dynamics applied to the 1-D wave equation and the 1-D Euler equations. Students will learn how to utilize simulation tools for 2-D problems, including grid generation, 2-D Euler and Navier-Stokes solvers, and post-processing tools.
General method of instruction
Recommended preparation
Students are expected to write computer program codes. Familiarity with the equations of fluid mechanics is helpful to provide motivation for the course.
Class assignments and grading
