A novel 1D-FDTD scheme to solve the nonlinear second-order thermoviscous hydrodynamic model

In this paper, we present a novel and simple Yee Finite-Difference Time-Domain (FDTD) scheme to solve numerically the nonlinear second-order thermoviscous Navier–Stokes Continuity equations. their original form, these equations cannot be discretized by using Yee’s mesh, at least, easily. As it is known, use of mesh recommended because optimized in order obtain higher computational performance remains core many current acoustic FDTD softwares. propose rewrite aforementioned form. To achieve this, will substitution corollary. This procedure literature. Although can extended more than one dimension, focus only on one-dimensional solution validated with two analytical solutions Burgers equation: Mendousse mono-frequency Lardner bi-frequency solution. Numerical are excellently consistent solution, which demonstrates effectiveness our formulation.