Simulations of thermally induced photoacoustic wave propagation using a pseudospectral time-domain method

Most physical models used to evaluate thermally induced photoacoustic waves in biomedical applications are approximations based on assumptions necessary to obtain analytical results, such as thermal and stress confinements. In contrast, using numerical methods to solve the general photoacoustic wave equations gives detailed information on the wave phenomenon without requiring as many assumptions to be made. The photoacoustic wave generated by thermal expansion is characterized by the heat conduction theorem and the state, continuity, and Navier-Stokes equations. This study developed a numerical solution in axis-symmetric cylindrical coordinates using a pseudospectral time-domain scheme. The method is efficient for large-scale simulations since it requires only 2 grid points per minimum wavelength, in contrast to conventional methods such as the finite-difference time-domain method requiring at least 10~20 grid points. The numerical techniques included Berenger´s perfectly matched layers for free wave simulations, and a linear-perturbation analytical solution was used to validate the simulation results. The numerical results obtained using 4 grid points per minimum wavelength in the simulation domain agreed with the theoretical estimates to within an absolute difference error of 3.87 times 10^-2 for a detection distance of 3.1 mm.