Andrew A. Piacsek
Graduate Prog. in Acoust., Penn State Univ., 117 Appl. Sci. Bldg., University Park, PA 16802
An alternative to the Pestorius--Anderson algorithm based on FFT concepts for nonlinear wave propagation with dissipation is one that makes explicit use of finite difference schemes. In a relatively recent study, Dey [Adv. Comp. Meth. Part. Diff. Eq. 6, 382--388 (1987)] presented and examined various finite difference schemes for solving Burgers' equation u[sub t]+(beta)uu[sub x]=(delta)u[sub xx]. It is shown here that analogous schemes are applicable to a system of equations that arise when molecular relaxation is included into the formulation and which reduce to Burgers' equation when the phase velocity increments associated with relaxation are set to zero. Codes based on these schemes are described and implemented for the propagation through a homogeneous medium of a waveform initially resembling a step shock. The choice of the numerical scheme and the discretization can cause anomalous distortions in the waveform; techniques for minimizing such or of discarding them are discussed. A general discussion is given of the pros and cons of using finite-difference techniques rather than algorithms based on the two-step process involving Fourier and inverse Fourier transforms. [Work supported by NASA Langley Research Center.]