Source: https://jmrplens.github.io/phonometry/guides/sections/simulation/ Most of this library predicts a number; this section computes the **wave field itself**. A finite-difference time-domain (FDTD) solver integrates the linear acoustic equations on a 2D grid, so reflection, diffraction, interference, modal behaviour and refraction through inhomogeneous media all emerge from first principles. The solver is deterministic (identical inputs give bit-identical outputs on the same platform), validated against analytic oracles, and doubles as a cross-check engine for the closed-form models of the other sections. The single page of this section explains the numerical method (the staggered leapfrog scheme and its Courant stability bound), the building blocks (sources, probes, obstacles and boundary conditions, including the locally reacting real-impedance edge), when a wave-based simulation is worth its cost, what a 2D domain can and cannot say about a 3D problem, and how numerical dispersion sets the cells-per-wavelength resolution rule. A good way to read it is alongside the closed-form pages it cross-checks: the modal frequencies of [room acoustics](/phonometry/guides/room-acoustics/) reappear as peaks in a simulated room spectrum, the barrier insertion loss of [ground effect and barriers](/phonometry/guides/ground-barriers/) can be re-derived by placing an obstacle in the domain, and the ray bending of [atmospheric refraction](/phonometry/guides/atmospheric-refraction/) emerges from a height-dependent sound-speed profile. When a geometry is too irregular for those models (odd-shaped rooms, multiple barriers, mixed impedance ground), the simulation is the fallback that still gives a quantitative answer; when a closed form exists, prefer it, and use the solver to verify the assumptions it rests on. ## Pages in this section - [2D FDTD wave simulation](/phonometry/guides/fdtd-simulation/): the staggered-grid pressure-velocity FDTD method following Attenborough & Van Renterghem (2021) chapter 4, its sources, probes, obstacles and boundary conditions, the 2D limits and the numerical dispersion rule.