Abstract
An implicit time-marching finite-difference scheme is developed for computing the steady two-dimensional inviscid transonic flows with arbitrary shaped boundaries. Most 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 thee coefficient matrix is destroyed. 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, the shocked flows through a nozzle are calculated, and the results are compared with the one-dimensional theory.
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