Time-domain spline interpolation in a simulation of N-wave propagation through turbulence

A fully time-domain solution of the Khokhlov-Zabolotskaya-Kuznetzov propagation equation is illustrated using cubic spline interpolation of an exact implicit solution for nonlinearity, temperature fluctuations, and advection in the propagation direction. The spline interpolation method is benchmarked against a frequency-domain solution and found to have similar accuracy while offering about a 50% or higher speedup. The methods are evaluated by propagating Taylor shocks through turbulence in one dimension and by propagating N-waves through turbulence in two dimensions including relaxation and diffraction. The performance is superior to implicit finite differences.