Grid-Size Reduction in Flow Calculations on Infinite Domains by Higher-Order Far-Field Asymptotics in Numerical Boundary Conditions

摘要

An error analysis of the numerical calculation of the steady flow on an infinite domain around a given airfoil by a domain-splitting (= zonal) method is presented. 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 reductions in grid size are possible, if the usual far field asymptotic approximation is augmented by only a few extra terms in the approximate asymptotic far field solution.