An Implicit Time-marching Scheme for Transonic Flow

Abstract

An implicit time-marching finite-difference scheme is developed for computing steady two-dimensional inviscid transonic flows with arbitrary shaped boundaries. Most of the existing implicit time-marching schemes, including the Beam-Warming scheme, are unconditionally stable according to Neumann's stability criterion, but actually cannot take a sufficiently large Courant number, because the diagonally dominant condition of the coefficient matrix is lost. In the present scheme, in order to remove this restriction of the Courant number, the Robert-Weiss convective-difference scheme is applied in place of the Crank-Nicholson scheme in the Beam-Warming delta-form approximate-factorization algorithm. As a numerical example, shocked flows through a nozzle are calculated, and the results are compared with the one-dimensional theory.