7: Visualization and Output

[philipnickel]

Description

Implement visualization tools for the wave simulation including domain plotting, animations, and diagnostic outputs.

Tasks

• Implement coordinate transform for plotting
  • Map (x, σ) to (x, z) using z = σ·d - h
• Plot solution on deformed physical mesh
• Plot free surface elevation η(x, t)
• Create animation of wave evolution
• Implement energy computation (kinetic + potential)
• Time series output at specified gauge locations

Acceptance Criteria

• Physical domain plot shows correct surface position
• Animation runs smoothly for standing wave case
• Energy plot shows conservation (small drift)
• Gauge output matches surface elevation at specified x locations

Deliverables

• plot_domain(Φ, η, h) function
• plot_surface(η, t) function
• animate_simulation(η_history) function
• Standing wave animation (GIF or MP4)