Accurate Time-Varying Sources in K-Space Pseudospectral Time Domain Acoustic Simulations

Abstract

The pseudospectral time domain (PSTD) method is popular as a wave equation solver, one of its advantages being that it permits the use of coarse grids, as long as the spatial sampling is greater than two points-per-wavelength. The k-space PSTD method improves on this by incorporating an additional factor to remove the numerical dispersion which arises from the discretisation of the time derivatives. However, the effect of the temporal discretisation of time-varying sources has not previously been considered, although it can lead to substantial errors in the predicted field unless the timestep is sufficiently small to ensure the highest frequency is sampled at many points-per-period. Here, a correction factor is derived which eliminates this source of error, resulting in a k-space PSTD method that retains the spatial sampling advantage of conventional PSTD schemes but is also accurate as long as the temporal sampling is greater than two points-per-period and the CFL number is < 1.

Benchmark problems for transcranial ultrasound simulation: Intercomparison of compressional wave models

“…Sources are modeled as free-field monopoles (injection of mass) using a staircase-free formulation to represent the bowl and piston geometries, 47 and a dispersion-corrected timestepping scheme. 52 Benchmarks 1 to 6 were computed using the axisymmetric version of k-Wave to provide a high-resolution reference simulation. 53 Benchmarks 1, 2, 3, and 5 used 60 PPW and 2400 PPP, while benchmarks 4 and 6 used 60 PPW and 6000 PPP.…”

Experimental Validation of k-Wave: Nonlinear Wave Propagation in Layered, Absorbing Fluid Media

“…In terms of the simulations, the way in which the source is defined in k-Wave was modified to reduce errors arising from the use of Dirichlet boundary conditions in pseudospectral time domain solvers [30]. A correction was also implemented to reduce error in time-varying sources [29], and other minor bug fixes have been implemented in new k-Wave releases. This iterative process will continue in future experimental validation and k-Wave development.…”

“…This solves a system of first-order equations accounting for nonlinearity, medium heterogeneities, and power law absorption, using a k-space pseudospectral method [7]. For all simulations, a k-space correction was also applied to the time varying source to remove the error due to the temporal sampling of the source function [29].…”