https://github.com/mooiman/delta-formulation

Numerics based on delta-formulation for time-integration
https://github.com/mooiman/delta-formulation

delta-formulation fully-implicit shallow-water-equations swe

Last synced: 11 months ago
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Numerics based on delta-formulation for time-integration

• Host: GitHub
• URL: https://github.com/mooiman/delta-formulation
• Owner: mooiman
• License: gpl-3.0
• Created: 2024-12-30T15:03:02.000Z (over 1 year ago)
• Default Branch: main
• Last Pushed: 2025-07-09T15:36:50.000Z (11 months ago)
• Last Synced: 2025-07-09T16:45:47.931Z (11 months ago)
• Topics: delta-formulation, fully-implicit, shallow-water-equations, swe
• Language: C++
• Homepage:
• Size: 22.5 MB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

          
# delta-formulation

Numerics based on delta-formulation with fully implicit time-integration.

The fully implicit time integration is reached by an iterative Newton linearisation, but the behaviour of the Newton iteration depends on the smoothness of the data.

Therefor the data is adjusted in that way that the second derivatives of all data is smooth and is negiglible. 

This step in the procedure is called *regularization*.

And the numerical scheme is chosen to be central in space, no dissipation is added to the model by the numerical method, just higher order (third-order) dispersion.

After the regularization and the central discretization the numerical method is accurate (second order), reliable (numerical are small compared to errors in the mathematical model), efficient (Newton quadratic convergence), robust (fully implicit).