Wave Propagation Simulation

This project simulates 2-D surface waves on a 6 m × 6 m water domain by solving the wave equation ztt = c2(zxx + zyy) with fixed (zero-displacement) edges using an explicit finite-difference scheme. A short pulse (or sinusoid) at a chosen point generates circular ripples that reflect from the boundaries and form interference patterns; an optional rectangular pillar demonstrates scattering and “shadowing.” Results are shown as animated 3-D surfaces and 2-D contour maps, with brief mesh-refinement studies to illustrate numerical accuracy.

Stone Toss Simulation

3D wave simulation with a dropped “stone” at (4, 1); expanding ripples, pillar scattering, and boundary reflections.
Contour still A
Surface still A
Contour still B
Surface still B
Contour snapshots; the pillar scatters waves and leaves a low-amplitude “shadow” behind it.

Central Oscillator Mesh Refinement Study

dx=0.01, t=4 s
dx=0.01
dx=0.1, t=4 s
dx=0.1
dx=0.25, t=4 s
dx=0.25
Mesh comparison — Time = 4 seconds
dx=0.01, t=6 s
dx=0.01
dx=0.1, t=6 s
dx=0.1
dx=0.25, t=6 s
dx=0.25
Mesh comparison — Time = 6 seconds
dx=0.01, t=10 s
dx=0.01
dx=0.1, t=10 s
dx=0.1
dx=0.25, t=10 s
dx=0.25
Mesh comparison — Time = 10 seconds