Abstract: In this paper a method is given for calculating transonic nozzle flow with arbitrary nozzle wall shape and arbitrary back pressure by Total Variation Diminishing (TVD) scheme because oi its high accuracy and rapid convergence. The results of axisymmetrical and plane nozzle flow fields, shock and shock tree flow fields are obtained for a typical nozzle of two straight lines with convergent angle of 45° . divergent angle of 15° respectively connected smoothly with a circular arc whose non-dimensional radius of curvature is 0.625. The numerical results are in good agreement with experimental results and other numerical results. This method can be extended to unsteady transonic nozzle flow calculations and used for nozzle design of engineering application

Key words: transoic flow nozzle, difference meihods, shock