HPC Tier Module
Acoustic Wave Propagation (2D FDTD)
Propagate 2D acoustic waves on a staggered FDTD grid, wave speed and energy checked against theory.
See it run - a worked example, 100% in this browser tab
The problem
Acoustic prototyping needs fast wave-propagation experiments, but desktop codes are heavy to set up and offer no immediate, built-in check that the scheme is CFL-stable or that the measured wave speed matches theory.
The local-first solution
This plugin leapfrogs the first-order pressure-velocity acoustic system on a staggered Yee-style grid in your browser, enforces the 2D CFL bound, and leads with closed-form checks: continuum wave speed, arrival-time speed recovery, and a bounded energy envelope. Deterministic f64 math, nothing uploaded.
What it does
Staggered-grid leapfrog of dp/dt=-K div v and dv/dt=-(1/rho) grad p
Exact continuum wave speed c=sqrt(K/rho) used for every timing claim
Measured arrival-time speed recovery c_measured/c with numerical-dispersion diagnostic
2D CFL stability bound c*dt/dx <= 1/sqrt(2) checked and enforced
Discrete acoustic energy tracked with a max/min bounded envelope
Ricker-wavelet source plus selectable rigid or first-order absorbing boundary
Honest scope
EXACT: the wave speed, CFL bound, dt relation, and leapfrog update arithmetic. MEASURED and checked: the wave-speed recovery and energy envelope, where numerical dispersion makes c_measured a few percent low (expected and citable). The absorbing edge is a crude sponge, not a true PML, and leaves a small residual reflection. NOT modeled: heterogeneous/lossy/nonlinear media, true PML, 3D, or shear conversion. A teaching/validation solver, not a production acoustics code.
Authorities cited
- Yee, K. S. (1966). Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media. IEEE Trans. Antennas Propag. 14, 302-307. DOI 10.1109/TAP.1966.1138693. (The staggered-grid leapfrog scheme adapted here for the acoustic pressure-velocity system.)
- Virieux, J. (1986). P-SV wave propagation in heterogeneous media: velocity-stress finite-difference method. Geophysics 51(4), 889-901. DOI 10.1190/1.1442147. (The staggered velocity-stress / pressure-velocity acoustic FDTD scheme.)
- Taflove, A. & Hagness, S. C. (2005). Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. Artech House. (2D Yee Courant stability bound c*dt/dx <= 1/sqrt(2).)
- Kinsler, L. E., Frey, A. R., Coppens, A. B., Sanders, J. V. (2000). Fundamentals of Acoustics, 4th ed. Wiley. (Lossless wave equation and the phase speed c = sqrt(K/rho) / c = sqrt(B/rho).)
- Ricker, N. (1953). The form and laws of propagation of seismic wavelets. Geophysics 18(1), 10-40. DOI 10.1190/1.1437843. (The Ricker wavelet source, negative second derivative of a Gaussian.)
- Courant, R., Friedrichs, K., Lewy, H. (1928). Uber die partiellen Differenzengleichungen der mathematischen Physik. Math. Ann. 100, 32-74. DOI 10.1007/BF01448839. (The CFL stability condition.)
Run a verified wave experiment
Propagate the field in your browser with nothing uploaded, then route the speed-recovery and energy diagnostics into a Sandbox workspace or attach them to a Worklog case.