Accuracy analysis of the results of tests

[szaghi]

Here we can discuss our conclusions about the accuracy of the results obtained from each test.

Passed Tests

List of tests for which the results accuracy is as expected for the formal order of the numerical scheme employed:

• [ ] Lorenz' test:
  • [ ] explicit:
  • [ ] Adams-Bashforth;
  • [ ] Euler;
  • [ ] Leapfrog;
  • [ ] Runge-Kutta:
    • [ ] TVD/SSP;
    • [ ] Low Storage;
• [x] Oscillation test¹:
  • [x] explicit:
  • [x] Adams-Bashforth;
  • [x] Adams-Bashforth-Moulton;
  • [x] Euler;
  • [x] Leapfrog;
  • [x] Runge-Kutta:
    • [x] TVD/SSP (5 stages solver seems less acurate than the similar low storage 5 stages);
    • [x] Low Storage;
    • [x] embedded³;
• [ ] Burgers' test:
  • [ ] explicit:
  • [ ] Adams-Bashforth;
  • [ ] Euler;
  • [ ] Leapfrog;
  • [ ] Runge-Kutta:
    • [ ] TVD/SSP;
    • [ ] Low Storage;
• [x] 1D Euler test²:
  • [x] explicit:
  • [x] Adams-Bashforth;
  • [x] Euler;
  • [x] Leapfrog;
  • [x] Runge-Kutta:
    • [x] TVD/SSP;
    • [x] Low Storage;

      Issues

      1. Analysis completed: all solvers works as expected.
      2. Analysis not completed.
      3. It is necessary to define a methodology for measuring the accuracy of adaptive time step schemes.

[szaghi]

Hi all, I have refactored 1D Euler and Oscillation tests in order to facilitate yhe errors analysis for accuracy assesment. I have added some scripts (pytjon snd bash) for automating tbe errors analysis. Essentially I have completed the analysis for the oscillation test (that you csn easily reprofuce with scripts provided, tomorrow I will add more instructions): all seems reasonably, only the tvd/ssp runge-kutta solvers are not good as I exepected they were. I have introduced some results into the manuscript draft.

https://github.com/Fortran-FOSS-Programmers/FOODiE/blob/master/papers/announcement/errors_analysis/errors_analysis.sh

https://github.com/Fortran-FOSS-Programmers/FOODiE/tree/master/papers/announcement/errors_analysis/utilities-oscillation

https://github.com/Fortran-FOSS-Programmers/FOODiE/blob/master/papers/announcement/manuscript.tex#L215