ABSTRACT

The generalization of the numerical Godunov method to aeroacoustics problems associated with the calculation of sound waves generation and propagation in a compressible fluid is considered. Stated in the present paper is the problem of the variation of the exact solution of the Riemann problem (the problem about the decay of an arbitrary discontinuity in gas) at small perturbations of the initial data.We show that this problem has a unique solution, which can be obtained in an explicit, analytic, and rather compact form for arbitrary values of the initial data perturbations. The obtained solution specifies the resultant acoustic flux, which arises during the interaction of the uniform fields of small perturbations on the background of the decay of an arbitrary discontinuity. This allows us to construct an analogue to the Godunov method for the system of linearized Euler equations describing the evolution of the acoustic field on the background of the nonuniform main flow. The calculation results, which show the efficiency of the proposed method, are given.