HPC Tier Module
Acoustic Wave Propagation (2D FDTD)
Propagate 2D acoustic waves on a staggered FDTD grid, wave speed and energy checked against theory.
This tool runs inside GDBS HPC. What it computes and the authorities it applies are below.
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.)
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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.