An error analysis is presented of the numerical calculation of the steady flow on an infinite domain around a given airfoil by a domain-splitting (= zonal) method. This method combines a fully-conservative finite-difference approximation on a finite domain around the airfoil with an approximate asymptotic solution outside this finite domain. The errors are analyzed as a function of the accuracy of the approximate asymptotic expansion, of the distance to the airfoil of the far-field boundary of the finite domain and of the mesh size. The numerical experiments show that, for a given desired accuracy level, large reduction in grid sizes are possible, if the usual far-field asymptotic approximation (uniform flow plus first-order perturbation by a circulation vortex at infinity) is augmented by only a few extra terms in the approximate asymptotic far-field solution. In this way, considerable numerical efficiency improvements can be realized. It is expected that this conclusion can be generalized to many other applications where computations on infinite domains are performed.
|Number of pages||21|
|Journal||Journal of Engineering Mathematics|
|Publication status||Published - 1984|