9: Stream Function Wave Validation

[philipnickel]

Description

Validate the solver against exact nonlinear stream function wave solutions. This provides rigorous convergence testing for strongly nonlinear waves.

Background

Dean's stream function method (1965) provides exact solutions to the fully nonlinear water wave problem for periodic waves of permanent form. These solutions are valid up to near-breaking steepness.

Tasks

• Implement or integrate stream function wave solver
  • Option A: Implement Dean's iterative method
  • Option B: Use Fenton's Fourier method
  • Option C: Interface to existing library
• Generate solutions for test cases:
  • kh = 1, H/L = 10% of max steepness
  • kh = 1, H/L = 50% of max steepness
  • kh = 1, H/L = 90% of max steepness
• Convergence study procedure
  • Use stream function η, φ as exact reference
  • Freeze surface, solve Laplace, compare w̃
  • Measure error vs resolution
• Generate convergence plots

Acceptance Criteria

• Stream function solver produces valid wave solutions
• p-convergence: Exponential for H/L = 10%
• p-convergence: Exponential for H/L = 50% (may need more DOF)
• p-convergence: Converges for H/L = 90% (possibly reduced rate)
• h-convergence: O(h^P) for all steepness levels

Deliverables

• Stream function wave module/interface
• Convergence plots for each steepness level
• Table of errors vs resolution