Goals

• Finish and submit manuscript about ABCs for the piston problem.
• Have a fully working 2d implementation of Escalante’s disperisve system in Geoclaw.
• Test Geoclaw implementation with several real world experiments
• Get solid knowledge about Hyperbolic PDEs to take advantage of the Spring School as SUSTech.

Week-by-week plan

Sep 10-14:

• Complete some important experiments for the piston problem paper:
  • Couple Sharpclaw with Strang operator splitting to compare first and second order relaxation with far-field operators in a similar framework. [X]
  • Get an error comparison using a sponge layer of fixed size and varying damping rates for the far-field damping operator. This should show why we want to use relaxation instead of integrating the source term explicitly. The error is too large if we use a small damping rate, thus we require a large damping rate and we get artificial stiffness with an explicit time integrator. [X]
  • The relaxation step can be written as an artificial source term in the equations. There is no way to integrate this term explicitly (when it goes to infinity). Following Prof. Russo’s suggestion we integrate it implicitly to see what happens.I am using scipy’s RK23 for the source term instead of an implicit solver. Maybe I can implement a Fortran routine to integrate te source term implicitly so that it is not so expensive (maybe even modify the solver class to use an IMEX scheme?)

• Complete the introduction for the piston problem paper. [ ]

• Finish Chapter 1 of LeFloch’s book.[X]

Sep 17-21:

• Test numerically the damping of the nonlinear characteristic variables instead of the linear ones. [ ]
• Analyze the results from the error comparisons with all the updates applied the previous week. [ ]
• Finish Chapter 2 of LeFloch’s book. [ ]
• …