Timestep formula (Water Overlay): Difference between revisions

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Revision as of 16:33, 15 October 2019

An adaptive timestep is implemented according to Kurganov and Petrova (2007)[1]. At every timestep, the courant-number is kept smaller than 0.25 for every active computation cell.

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Especially at low depths, choosing the appropriate timestep is critical to avoid numerical instability. Therefore the following principles are used to determine the right time step:

  • the timestep is choosen so that all computation cells follow one of the following criteria.
  • if a cells waterdepth is below the flooding threshold, 5 * 10-3 (m) there is no flow assumed between that cell and it neigboring cell.
  • if the cells waterdepth is above above the flooding threshold, the maximum timestep is assumed to be 100 * the waterdepth at the cell.
  • if the waterdepth increases, the timestep is assumed to be not larger than the formula above.

If the numerical flux decreases, larger timesteps are allowed than set by Kurganov and Petrova[1], depending on the configured calculation.

References

  1. 1.0 1.1 Kurganov A, Petrova G (2007) ∙ A Second-Order Well-Balanced Positivity Preserving Central-Upwind Scheme for the Saint-Venant System ∙ p 15 ∙ found at: http://www.math.tamu.edu/~gpetrova/KPSV.pdf (last visited 2018-06-29)

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