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Feature/particle integration test

Merged Cristian Lalescu requested to merge feature/particle_integration_test into develop

Adds an in-depth convergence test for particle tracking of a stationary field.

In the below figure "o" stands for "solver order", "n" for interpolation neighbours and "m" for interpolation smoothness. This figure shows the result.

Notes:

  • I also added a classic Runge Kutta solver for particles, to emphasize effects of interpolation. The plot suggests that the implementation is correct (I need to see order 4 convergence to believe the code is correct).
  • The number of particles is relatively small now because otherwise the test is too slow in DEBUG mode. There seems to be a separate issue with optimization that I'll need to address.
  • The effects of the interpolation are only visible if the particle trajectories are long enough --- i.e. particles need to traverse a few grid cells in order for cell-crossing effects to show up. This is why there are so many iterations...
Edited by Cristian Lalescu

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