Mathematical Methods for Fluids, Solids and Interfaces (Spring 2009)

Date | Contents |
---|---|

2009-6-13 | Homework 9 solutions are now available. |

2009-6-02 | Lectures 17-19 are available, and Extra Credit 1, Homework 6 and 7 are graded and available. |

2009-5-28 | Extra Credit 2 has been posted. |

2009-5-27 | Typos fixed in homework 9; solutions to homework 7 and 8 posted. |

2009-5-26 | Minor clarification to Homework 9: density also lives at cell centers. |

2009-5-25 | Homework 9, Letures 15 and 16 are now available. |

2009-5-19 | Homework 5 has been graded and is available at Gates 377. |

2009-5-18 | Homework 8 and Lectures 13 and 14 are now available. |

2009-5-14 | Solutions to Homework 4,5 and 6 are now available. |

2009-5-13 | Homework 7 is now available. Please note that it is due Tuesday. |

2009-5-12 | Lecture 12 and Extra Credit assigment 1 are now available. |

2009-5-7 | Lectures 10 and 11 are now available. |

2009-5-7 | Homework 6 is posted. Note that it is due Thursday next week. |

2009-5-5 | Lecture 10 has been posted. |

2009-4-30 | Homework 3 and 4 have been graded and are now available at Gates 377. |

2009-4-28 | Lecture 9 and Homework 5 are posted. |

2009-4-26 | Homework 4 has a typo; the online version is now correct. |

2009-4-25 | Homework 3 solutions have been posted. |

2009-4-21 | Lectures 6, 7 and 8 have been posted, and homework 4 is now available. |

2009-4-15 | Homework 2 has been graded and is available at Gates 377, and solutions have been posted. |

2009-4-14 | Lecture 5 and Homework 3 are posted. Graded homework 1 will be available by the end of the day, and solutions to homework 2 will be posted by noon. |

2009-4-10 | Lecture 4 is posted. |

2009-4-09 | Homework 1 solutions posted. |

2009-4-08 | Several mistakes in the homework assignment have been fixed. In particular, you are asked do rederive the weak form of conservation of mass, not momentum in the first section of the assignment, and the method is Runge, not Runga. |

2009-4-08 | Discussion section notes will not be posted this week. The material covered was the Lax-Richtmyer framework (which is covered in Discussion 1), and Runge-Kutta (of which everything I covered is provided in the homework itself. |

2009-4-07 | Homework 2 and Lecture 3 are posted. |

2009-4-02 | Several minor changes have been made to the Discussion Section; please read the description and note that an additional section has been added that will cover the same material as the Wednesday section. |

2009-4-02 | Lecture 2 is posted. |

2009-4-02 | The theory section has been updated -- please note that Jón will be covering his material again during Friday office hours. |

2009-3-31 | Homework 1 is posted. |

2009-3-31 | Website is live! |

Overview of numerical methods for the simulation of problems involving solid mechanics and fluid dynamics. The focus is on practical tools needed for simulation, as well as the necessary continuous mathematics involving nonlinear hyperbolic partial differential equations. Possible topics include the finite element method, highly deformable elastic bodies, plasticity, fracture, the level set method, Burgers' equation, compressible and incompressible Navier-Stokes equations, smoke, water and solid-fluid coupling.

- Instructor
- Ron Fedkiw (fedkiw@cs.stanford.edu)
- Office: Gates 207
- Office hours: After class (10:45AM-11:45AM)

- Course Assistants
- Jón Tómas Grétarsson (jontg@stanford.edu)
- Office hours:
- Tuesday (12:00PM-1:00PM Gates 207,
- Friday (4:00PM-5:00PM Gates 200)

- Craig Schroeder (cas43@cs.stanford.edu)
- Office hours location: Gates 200 or 209
- Office hours: Tuesday, Friday (1:00PM-2:00PM)

Please refer all questions about course material and practices to the CAs
**before** contacting Professor Fedkiw. If you have a question for the CAs,
please make sure that it isn't answered on this webpage before contacting them.
Also, please do not show up outside of scheduled office hours without first
making an appointment. When emailing the CAs, make sure to include "CME306" or
"CS205B" somewhere in the subject of your message.

- Class: Tuesday and Thursday, 9:30AM-10:45AM in 260-113
- Theoretical Section: Wednesday, 5:30PM-6:30PM in Gates 104, and again Friday from 3:00PM-4:00PM in Gates 200
- Applied Section: Thursday, 5:00PM-6:00PM in Gates 463a

*Finite Volume Methods for Hyperbolic Problems*, by Randall J. LeVeque, Cambridge University Press 2002.*Finite Difference Schemes and Partial Differential Equations*(2nd ed.), by John C. Strikwerda, SIAM 2004.The first chapter of this book is available on the SIAM website, and is on permanent reserve at the Mathematical and Computer Science Library.

*Level Set Methods and Dynamic Implicit Surfaces*, by Stanley Osher and Ronald Fedkiw, Springer 2003.- Mathematical Models: Mechanical Vibrations, Population Dynamics and Traffic Flow, by Richard Haberman, SIAM 1998

Class | Description |
---|---|

Lecture 1 | Introduction, Simulation of Materials |

Lecture 2 | Conservation of Mass, Smoothed Particle Hydrodynamics |

Lecture 3 | Smoothed Particle Hydrodynamics, Forces, Linearized System |

Lecture 4 | Ordinary Differential Equations, Stability, Newmark Methods |

Lecture 5 | Springs |

Lecture 6 | Springs |

Lecture 7 | Finite Element Method |

Lecture 8 | Finite Element Method, Rigid Bodies |

Lecture 9 | Advection, Runge-Kutta, Hamilton-Jacobi ENO, Semi-Lagrangian Advection |

Lecture 10 | Hyperbolic Conservation Laws, Shocks and Rarefactions |

Lecture 11 | Discrete Conservation Form, ENO-Roe, ENO-LLF |

Lecture 12 | Discrete Conservation Form, ENO-Roe, ENO-LLF |

Lecture 13 | Multiple Dimensions, Systems |

Lecture 14 | Systems, Discretizations, Shallow Water |

Lecture 15 | Incompressible Flow Equations |

Lecture 16 | Incompressible Flow Equations: the Poisson Equation |

Lecture 17 | Incompressible Flow Equations: Discretization, Semi-Lagrangian Advection |

Lecture 18 | Heat Equation |

Lecture 19 | Viscosity, Vorticity |

In addition to lecture, there will be a section run on Wednesday from 5:30PM to 6:30PM and repeated on Friday from 3:00PM to 4:00PM, which covers tools necessary for the completion of the theory-track homework. While not manditory, it is strongly recommended for any students who intend to take the iCME Qualifying Exams.

Class | Description |
---|---|

Discussion 1 | Convergence, Consistency and Stability, Von Neumann analysis, and the Lax-Richtmyer Equivalence Theorem |

Discussion 2 | Modified Equations, Dissipation vs. Dispersion, Rigid Body Rotations |

There will be a problem set assigned each week which will be posted on
Tuesday at 11:00AM. There are two separate tracks of homework: theory (which
involves more qualifying exam preparation), and application (which involves
more software development). If you are taking the iCME qualifying exams, you
are **strongly** encouraged to take the theoretical track. If you are
looking for the application homework, take a look at CS 205B.

Homework will be graded in coarse, half-point increments between 0 and 2 points.

You may collaborate on homework assignments provided each student writes up his or her own solutions and clearly lists the names of all the students in the group.

Theoretical | Due Date |
---|---|

Homework 1(tex) (Solution) | 2008-4-7 |

Homework 2(tex) (Solution) | 2008-4-14 |

Homework 3(tex) (Solution) | 2008-4-21 |

Homework 4(tex) (Solution) | 2008-4-28 |

Homework 5(tex) (Solution) | 2008-5-5 |

Homework 6(tex) (Solution) | 2008-5-14 |

Homework 7(tex) (Solution) | 2008-5-19 |

Homework 8(tex) (Solution) | 2008-5-26 |

Homework 9(tex) (Solution) | 2008-6-2 |

Homework must be submitted physically either in class or in the bin outside Gates 204 by 11 AM. Graded homework will be available for pickup in the Gates 377 filing cabinets.

Depending on class performance on homework and exams, there will be a small number of optional extra credit assignments. These assignments will require you to implement some of the numerical schemes discussed during the course. Extra credit projects do not have a set point value; rather, they will be taken into account at the end of the quarter when determining your final letter grade.

Please note that you are free to do, as extra credit, the homework from the applied track.

Assignment | Due Date |
---|---|

Extra Credit 1(tex) | 2008-5-26 |

Extra Credit 2(tex) | 2008-6-4 |

The final grade will be calculated based on the **highest** score between
your theoretical and applied homework. The lower of the two will be counted
towards extra credit. You should complete either **all** of the theoretical
or **all** of the applied homework, not a mix of the two.