RESEARCH ON NONLINEAR ACOUSTICS

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...

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Bibliographic Details
Main Authors: Ablow,Clarence M, McCulley,Leonard D, Muller,George M, Penico,Anthony J, Rajapakse,Yapa D
Format: Report
Language:English
Subjects:
Acoustics
APPROXIMATION(MATHEMATICS)
BOUNDARY VALUE PROBLEMS
COMPLEX NUMBERS
COMPUTER PROGRAMMING
CONVERGENCE
FLOW FIELDS
ITERATIONS
MATHEMATICAL ANALYSIS
NONLINEAR PROGRAMMING
NONLINEAR SYSTEMS
NUMERICAL ANALYSIS
Numerical Mathematics
PARTIAL DIFFERENTIAL EQUATIONS
PERIODIC VARIATIONS
SOUND
SPECIAL FUNCTIONS(MATHEMATICAL)
SUBROUTINES
VECTOR ANALYSIS
WAVEFORM GENERATORS
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Summary: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)