IMPLEMENTATION OF HIGH-ORDER COMPACT SCHEMES TO THE ITERATIVE PARABOLIZED NAVIER-STOKES EQUATIONS

摘要

The numerical solution of the parabolized Navier-Stokes (PNS) and globally iterated PNS (IPNS) equations for accurate computation of hypersonic axisymmetric flowfields is obtained by using the fourth-order compact finite-difference method. The PNS and IPNS equations in the general curvilinear coordinates are solved by using the implicit finite-difference algorithm of Beam and Warming type with a high-order compact accuracy. A shock fitting procedure is utilized in both the compact PNS and IPNS schemes to obtain accurate solutions in the vicinity of the shock. The main advantage of the present formulation is that the basic fiow variables and their first and second derivatives are simultaneously computed with the fourth-order accuracy. The computations are performed for a benchmark case; hypersonic axisymmetric flow over a blunt cone at Mach 8. The present results for the flowfield variables and also their derivatives are compared with those of the second-order method and accuracy analysis is performed to insure the fourth-order accuracy of the proposed method. A sensitivity study is performed for the basic flowfield, including profiles and their derivatives obtained from the fourth-order compact PNS and IPNS solutions, and the effects of grid size and numerical dissipation term used are discussed. The present work represents the firstknown application of a high-order compact finite-difference method to the PNS schemes which are computationally'more efficient than Navier-Stokes solutions.