Ma4620 Project List

If anyone has anything they want to add talk to me.  The rules are two people work together in declared teams.  An organizational proposal needs to be prepared over the Thanksgiving break:  this should consist of a list of the equations; a proposed discretization; some discussion of how any unique problems will be addressed; a sketch (with some indiaction of mode numbering nd boundary conditions); some comprehensible test problem; and a list of hoped for results.  The due date for projects is Friday of finals week at noon.  These projects are not of equal difficulty!  It is perfectly possible that some of these projects will not work out quite the way we hope!  I would like to have people make brief presentations (5-10 minutes) to the class about their projects on Monday of finals week during our scheduled final time slot:  Everyone needs to attend this cause you are going to grade each others presentations. I propose that the projects be graded: 40% on that presentation (graded by the rest of the class on a 10 pt scale);  40% on the final results and code (judged by me); and 20% on the organization of the organizational proposal (judged by me).  I am open to suggestions for modifications.

1.  Fluid Flow Past an Obstacle.

2D creeping flow of a fluid past an obstacle. 
Extension remove creeping! 
Main problem boundary conditions

2.  Earthquakes

Simulate earthquake propagation. in a flat layered geometry.
Main problem 3 dimensional and lots of tricky equations

3.  Freezing pipes

Use cylindrical geometry to simulate the freezing of a fluid in a cold pipe.
Main problem is nonlinearity and coupled equations.

4.  Nonlinear Shroedinger Equation

Simulate the solution of the cubic NLS equation.
Main problem is nonlinearity

5.  Korteweg de Vries Equation

Simulate the solution of the kdv equation.
Main problem is nonlinearity.

6.  Tidal Surge and Bores

Simulate the solution of a surge equation.
Main problem is geoemetry of boundary and implementation of boundary conditions.

7.  Rotating Cylinder Flows: Taylor-Couette Instability

Simulate fluid flow equations in a cylindrical geometry. 
Main problem is non-linearity.

8.  JAWS:  Simulation of surface wave focusing based on undersea features.

Simulate the solution of a surface wave equation.
Main problem is spatial dependence of the coefficients.

9.  Simulation of convection cells.

Simulate the coupled slow flow / heat induce bouyancy equations.
Main problem is coupling

10.  Igor Kliakhandlers's Droplets

Coupled and unusual equations
Main problem the possibility that the solutions do not match well with the pics. :(