Accounting for Viscous and Thermal Effects in Time Domain in Computational Acoustic Problems

The problem of acoustic wave propagation with thermoviscous boundary conditions is studied. For thermoviscous boundary conditions, a time-domain formulation is formulated based on the concept of a fractional derivative. A weak formulation of the problem is given, which is reduced to a system of Volterra-type integro-differential equations using the finite element method. An implicit finite-difference scheme is constructed for the numerical solution of this system. To verify it, the problem of sound propagation in a thin pipe is modeled, and the results of numerical modeling are compared with the analytical solution