An Efficient Time-Marching Scheme for Solving Compressible Euler Equations

An implicit time-marching finite-difference scheme is proposed for analysing steady two-dimensional inviscid transonic flows. The scheme is based on the well-known Beam-Warming delta-form approximate factorization scheme, but this is improved on the following two points: ( i ) In order to treat the fixed wall boundary condition without difficulty, momentum equations of contravariant velocity components as fundamental equations in curvilinear coordinates are used. (ii) To calculate stably with a sufficiently large Courant number, the central-difference of the Crank-Nicholson method is replaced by the upstream-difference of the Robert-Weiss method. The upstreaming is performed on the basis of the theory of characteristics and does not influence the accuracy of the solution. The flows through a converging-diverging nozzle and over a symmetric wing are calculated. The calcutated results agree well with the existing theories.