Numerical Simulation of 2D Acoustic Wave Equation

We can utilize the regular grid finite difference method to simulate acoustic wave propagation. This numerical approach discretizes continuous space into a structured grid system, where wave propagation calculations are performed at each grid point. The implementation typically involves solving the 2D acoustic wave equation using central difference schemes for both temporal and spatial derivatives. Key algorithmic components include: 1) Velocity field initialization representing material properties, 2) Wavefield update using staggered grid finite differences, 3) Boundary condition handling (such as absorbing boundaries using PML implementation), and 4) Source injection mechanisms. By computing wave propagation at each grid cell, we can accurately simulate comprehensive wave phenomena including reflection, refraction, and diffraction effects. This methodology finds extensive applications in seismic exploration, acoustic imaging, and non-destructive testing, where the core implementation often leverages optimized matrix operations and parallel computing techniques for efficient large-scale simulations.