WaveSim

1D and 2D wave simulation from scratch. For more details, please check out this YouTube video.

The repository is setup as a package with source code in the folder named src.

Before running the demo files, please add this package to your Julia global environment.

• To run the 1D wave equation demo, please open app_1d.jl file in Pluto notebook.

• To run the 2D wave equation demo, please open app_2d.jl file in Pluto notebook.

Quick instructions for adding WaveSim package to the global environment

WARNING: The instructions below might not work, so please do check out the official Julia programming language webpage for instructions.

• Open Julia in the terminal and make sure that the working directory is WaveSim folder.
• Move to the Pkg manager by pressing ] key.
• Execute dev . command. This should add WaveSim to the global environment.
• Execute instantiate command.
• Go back to the Julia prompt and open Pluto notebooks.

Topics

• 1D Wave Equation
  • Finite Difference Method
  • Simulation Accuracy and Stability
    • Numerical Dispersion
    • Fine vs. coarse grid
    • Higher-order Finite Difference approximations
    • Von Neumann Analysis
  • Boundary Conditions
    • Dirichlet boundary condition
    • Neumann boundary conditions
    • Absorbing boundary conditions
• 2D Wave Equation
  • Finite difference method for 2D problem
  • Heterogeneous medium
  • Simulation Accuracy and Stability
    • Numerical Dispersion
    • Fine vs. coarse grid
    • Higher-order Finite Difference approximations
    • Von Neumann Analysis
  • Boundary Conditions
    • Dirichlet boundary condition
    • Neumann boundary conditions
    • Absorbing boundary conditions

References

• FDM 5-point stencil
• Excellent resources on Von Neumann analysis:
  • MIT notes
  • Jeff Chasnov's YouTube video
  • LMU Seismology
• Absorbing boundary condition