Accession Number : AD0675945

Title :   NUMERICAL SOLUTIONS OF THE SCALAR HELMHOLTZ EQUATION.

Descriptive Note : Technical rept.,

Corporate Author : HOUSTON UNIV TEX DEPT OF MECHANICAL ENGINEERING

Personal Author(s) : Boyd,J. H. , Jr. ; Childs,B.

Report Date : AUG 1968

Pagination or Media Count : 53

Abstract : Numerical methods for solving the scalar Helmholtz equation have been investigated and are discussed in this report. These methods are applicable to many realistic acoustic radiation problems. It is shown that boundary conditions of the first and second type are easily handled; the Sommerfeld radiation condition was also successfully utilized as an external boundary condition, using a complex velocity potential. The strategies used with the method of particular solutions provide a direct method for solving these problems. This method is illustrated by solving the classical acoustics problem of a spherical piston. The results obtained are shown to be in good agreement with the analytical solution. The method is also applied to the problem of a flat piston set in a sphere, and the results appear to be reasonable. Investigation revealed that least-squares filtering applied to the finite-difference operators can effectively reduce the growth of truncation errors. (Author)

Descriptors :   (*ACOUSTICS, WAVE PROPAGATION), (*PARTIAL DIFFERENTIAL EQUATIONS, NUMERICAL ANALYSIS), VIBRATION, PISTONS, SPHERES, PERTURBATION THEORY, BOUNDARY VALUE PROBLEMS, BOUNDARY VALUE PROBLEMS, LEAST SQUARES METHOD, WAVE FUNCTIONS, CONVERGENCE, ERRORS, THESES

Subject Categories : Statistics and Probability
      Acoustics

Distribution Statement : APPROVED FOR PUBLIC RELEASE