### ASA 124th Meeting New Orleans 1992 October

## 3aPA14. Finite-difference and Pestorius algorithms for solving nonlinear
propagation equations with molecular relaxation included.

**Andrew A. Piacsek
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*Graduate Prog. in Acoust., Penn State Univ., 117 Appl. Sci. Bldg.,
University Park, PA 16802
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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.]