This course addresses how to write and maintain a high-performance, high-fidelity, readily extensible numerical simulation code to study complex 2D and 3D laminar and turbulent flow phenomena in simple geometries. After some warm-up exercises, the focus of our efforts is on the group development of a powerful open-source code named diablo. Though the sometimes chaotic and multiscale flow phenomena that diablo simulates are ubiquitous in science and engineering, the focus of the class itself is on the accurate and efficient numerical simulation of the 3D Navier-Stokes equation on modern computational hardware.
The class leverages several of the basic numerical methods presented in MAE290a/b, including
- CN, RK, and IMEX timestepping methods, and
- finite difference spatial discretization methods.
In addition, we introduce a few additional advanced numerical methods including
- spectral methods and the FFT, and
- multigrid methods for elliptic systems.
In MAE223, we use these methods to extend diablo to several interesting new classes of problems.
Time and place: In Spring 2012 (Class Section ID: 743138), MAE223 will be taught Tu/Th 8-9:20 in 584 ebu1.
Instructor: Thomas Bewley; Office hours: MWF 8-9am in Prof. Bewley's office, 1805 ebu1.
Administrative details: There are a couple of individual projects and a final group project. Students who have taken this course in the past, with a different professor, are encouraged to participate (as the focus of Prof. Bewley's offering of this class is quite different), and may sign up for independent study units as MAE 296 or 299.
Text: This class is taught from selected sections of Numerical Renaissance, focusing in particular on the development of diablo, with supplemental texts held on reserve at the library as announced in class, including:
Computational Techniques for Fluid Dynamics (Fletcher)
Spectral Methods in Fluid Dynamics (Canuto et al.)
Chebyshev and Fourier Spectral Methods (Boyd)
Essential CVS (Vesperman)
Course goals: By the end of this course, students will understand how to solve the discretized Navier-Stokes equations using mixed explicit/implicit time-stepping methods, both finite difference and spectral spatial discretization methods, and multigrid methods for solution of the associated Poisson equations. While the focus of most of the course will be on the direct numerical simulation of incompressible flows in simple geometries, advanced topics such as large eddy simulation, turbulence modeling, immersed boundary methods, density-driven flows, parallel computations, etc., will be explored during lectures later in the quarter, and will form the subjects of the final group projects. The class is designed such that many students will be able to use the collective result of their class projects in their own research (many students who have previously taken this class from Prof Bewley have gone on to do exactly that).
Prerequisites: Graduate-level numerical methods (MAE290a, MAE290b). A background in graduate-level fluid mechanics is useful but not required.
Policies: Please read the Course & Homework Policy for this class.
