Improved Characteristic-based Solutions of the Euler Equations in Transonic Regimes

Abstract

A finite-volume computer code has been developed for solving the Euler equations in transonic regimes. In this code, the convective terms are modeled by a novel compound characteristic-based scheme which has a wide range of stability and enhanced accuracy. Thereby first- and second-order pressure-based flux weighting factors are employed which have an upwind-biased effect and achieve a consistent modeling of the information propagation. The discretized equations are advanced in time by a fifth-order Runge-Kutta algorithm. The implementation of the proposed method has led to a reduction of convergence steps. This was shown by application of the new method to flows over a NACA 0012 airfoil at different angles of attack and a circular cylinder. The solutions are compared with available data and favorable agreement is observed. The results have also shown that the numerical solution of the Euler equations can result in vortical flow behavior, as discussed further in (Razavi and Nozari Int. Review Mech. Eng. 3, 702-708 (2009)).