On inclusion of source in the system of first-order linear wave equations

Simulating propagation of acoustic waves via solving a system of three-coupled first-order linear differential equations using a k-space pseudo-spectral method is popular for biomedical applications, firstly because of availability of an open-source toolbox for implementation of this numerical approach, and secondly because of its efficiency. The k-space pseudo-spectral method is efficient, because it allows coarser computational grids and larger time steps than finite difference and finite element methods for the same accuracy. The goal of this study is to compare this numerical wave solver with an analytical solution to the wave equation using the Green's function for computing propagation of acoustic waves in homogeneous media. This comparison is done in the frequency domain. Using the k-Wave solver, a match to the Green's function is obtained after modifying the approach taken for including mass source in the linearised equation of continuity (conservation of mass) in the associated system of wave equations.