A steady, shock–capturing pressure–based computational procedure for inviscid, two–dimensional transonic flows

The present study describes a method for the prediction of steady, transonic, two–dimensional fluid flow in planar nozzles. The present work is essentially an extension of earlier work by Parameswaran [1] to two dimensions. The steady Euler equations are expressed on a nonorthogonal grid system formed by streamlines and lines parallel to the y axis. Grid–based velocity components are employed to represent the velocity field of the flow. The differential equations are discretized in a finite–volume fashion. A partially staggered grid system is employed to store the variables. The upwind differencing scheme is employed to approximate the convective terms. A modified version of the SIMPLE algorithm is employed to solve the coupled, nonlinear equations. For flows with shocks, a novel procedure is employed to capture the shock within a cell on each stream tube.