A FRAMEWORK FOR EVALUATING BOUNDARY CONDITIONS

Abstract

This paper explores solutions to the spherically symmetric Euler equations. Motivated by the work of Hagstrom and Hariharan7 and Geer and Pope,5 we model the effect of a pulsating sphere in a compressible medium. The literature available on this suggests that an accurate numerical solution requires artificial boundary conditions which simulate the propagation of nonlinear waves in open domains. Until recently, the boundary conditions available are in general linear, and based on non-reflection. Exceptions to this are the nonlinear nonreflective conditions of Thompson,11 and the nonlinear reflective condition of Ref. 7. The former is based on the rate of change of the incoming characteristics, while the latter relies on asymptotic analysis and the method of characteristics and accounts for the coupling of incoming and outgoing characteristics. Furthermore in Ref. 7 it was shown in a test situation in which the flow would reach a steady state over a long time, the method proposed in Ref. 11 could lead to an incorrect steady state. The current study considers periodic flows. Moreover, various other types and techniques of boundary conditions are included in this study. The technique recommended by Ref. 7 proved superior to all others considered, and matched the results of asymptotic methods which are valid for low subsonic Mach numbers.