Acoustic Wave Propagation in Two-Dimensional Isotropic Media

This document demonstrates the application of finite difference methods to solve wave equations, producing numerical simulation results including waveform data and wavefield animations. The simulation employs central difference schemes for spatial derivatives and time-stepping algorithms like leapfrog or Runge-Kutta methods for temporal evolution. These simulations provide valuable insights into wave phenomena and offer practical guidance for real-world applications. Through numerical solution of the wave equation, we obtain wavefield variations across different temporal and spatial coordinates, revealing propagation patterns and characteristics of acoustic waves. The implementation typically involves discretizing the computational domain using staggered grids and applying appropriate boundary conditions (e.g., absorbing boundary conditions) to minimize reflections. Wavefield animations visually demonstrate wave behavior and evolution processes, enabling deeper investigation and analysis of wave phenomena. The finite difference approach for numerical simulation of wave equations proves to be an effective and practical methodology, widely applicable in seismology, acoustics, optics, and related research fields. Key computational aspects include stability analysis through Courant-Friedrichs-Lewy (CFL) conditions and parallelization techniques for large-scale simulations.