Accession Number : AD0667223
Title : RESEARCH ON NONLINEAR ACOUSTICS.
Descriptive Note : Final rept. 15 Nov 64-15 Sep 66,
Corporate Author : STANFORD RESEARCH INST MENLO PARK CALIF
Personal Author(s) : Ablow,Clarence M. ; McCulley,Leonard D. ; Muller,George M. ; Penico,Anthony J. ; Rajapakse,Yapa D.
Report Date : DEC 1967
Pagination or Media Count : 189
Abstract : The possibility that nonlinear acoustic flows may be represented by spherical progressive waves (in the sense of Courant and Friedrichs) was examined and found to be unlikely. An iterative finite-difference method for the calculation of continuous periodic spherical flows was developed together with a FORTRAN code, SPHERE, that implements the method. Sample calculations have shown that the code is effective but slow, and several ways for reducing the computation time are suggested. Convergence difficulties in one of the iterative loops were overcome by the use of a semi-iterative underrelaxation scheme. When applied to linear systems, such semi-iterative schemes were found to be equivalent to a class of summability methods that may be regarded as generalizations of Euler summation. (Author)
Descriptors : (*ACOUSTICS, NONLINEAR SYSTEMS), (*FLOW FIELDS, MATHEMATICAL ANALYSIS), SOUND, NUMERICAL ANALYSIS, COMPUTER PROGRAMMING, SPECIAL FUNCTIONS(MATHEMATICAL), VECTOR ANALYSIS, COMPLEX NUMBERS, ITERATIONS, PERIODIC VARIATIONS, PARTIAL DIFFERENTIAL EQUATIONS, BOUNDARY VALUE PROBLEMS, APPROXIMATION(MATHEMATICS), NONLINEAR PROGRAMMING, SUBROUTINES, CONVERGENCE, WAVEFORM GENERATORS
Subject Categories : Numerical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE