10: Variable Bathymetry Support #20
Description
Description
Extend the solver to support spatially varying water depth h(x). This is required for the submerged bar benchmark.
Background
With variable bathymetry:
- d(x,t) = η(x,t) + h(x)
- K matrix components now vary with x through both η and h
- May want to align element boundaries with bathymetry discontinuities (slope changes)
Tasks
- Modify depth from scalar to function/array h(x)
- Update d(x) computation to use h(x)
- Update K matrix computation
- Implement piecewise linear bathymetry definition
- Test with simple sloping bottom
- Test with bar geometry
Acceptance Criteria
- Constant h(x) = h₀ gives same result as before
- Sloping bottom: solution remains physical (no instability)
- Bar geometry: waves shoal and steepen as expected
- No spurious reflections from bathymetry changes
Technical Notes
- Consider placing element boundaries at slope transitions
- The bottom BC ∂ₙΦ = 0 should still be natural in weak form
- Sharp bathymetry changes may need special treatment