Effects of Imposing Higher-Order Far-Field Boundary Conditions on the Numerical Solution of the Two-Dimensional Compressible Euler Equations.

Abstract

Higher-order far-field boundary conditions utilizing the Riemann-like variables have been applied for solving the two-dimensional compressible Euler equations. The governing equations are discretized by a central finite-difference approximation and integrated by the rational Runge-Kutta (RRK) scheme. Higher-order far-field computational boundary conditions in external flows presented by Verhoff et al. are incorporated into the basic scheme in order to investigate the effects on the numerical solution. Numerical calculations are carried out for external flows past a NACA 0012 airfoil at the uniform flow Mach number M∞=0.55, angle of attack α=2°, M∞=0.8 and α=1.25°.Compared with the conventional low-order far-field boundary conditions, the present method gives a comparable lift coefficient (CL) and pressure coefficient (CP) with a much smaller number of grid points, while it shows a slower convergence rate. It is found that this yields reduction of the number of grid points by approximately 50∼70% and total CPU time by 50∼70% in obtaining comparable results.