Discretization Errors in the Far Field Conditions for Oscillatory Subsonic Flows.

Abstract

Abstract : In their complete form, far field conditions are given by an infinite number of global linear equations between the potential and its normal derivative at the far boundary of the computed part of a flow field. This report illustrates the effects of a discretization carried out in the partial differential equation for different formulations of the far field conditions. If one considers the potential and its normal derivative at all points of the far boundary as infinite vectors, then the far field conditions are established by the infinite matrices. The appearance of these matrices depends upon the choice of the 'test' functions used in formulating the far field conditions, but the relations obtained for different formulations arise from each other by premultiplication with some matrix. In a numerical approach an approximation of the potential and its normal derivative in terms of a finite number of parameters must be used, the vector is restricted to a finite dimensional subspace. The matrices encountered in formulating the far field conditions depend upon the choice of the subspace and of the relative eigenvectors and eigenvalues of the two matrices. For vectors in an infinite vector space they are independent of the choice of the test functions. The effect of the discretization can be recognized by the deviation of the eigenvectors and eigenvalues from the ideal case.