Finite volume solution of the two-dimensional euler equations on quadrilateral and triangular meshes.

Abstract

The two-dimensional Euler equations have been solved by a finite volume method (FVM). The computational domain is divided into either quadrilateral or triangular cells. Spatial discretization of the Euler equations on each cell yields a system of ordinary differential equations (ODEs) in time. A rational Runge-Kutta (RRK) scheme is used to integrate the system of ODEs. The implicit residual averaging (IRA) and local time step have been employed to accelerate the convergence to a steady state. Numerical solutions are presented for flows past a circular cylinder at Mach 0.38, the NACA 0012 airfoil at Mach 0.8 and an angle of attack of 1.25°, and a channel flow at Mach 0.675. The effects of the shape of control volume and convegence acceleration techniques are investigated by comparing the results with those of the conventional finite difference discretization method (FDM). It is concluded that accuracy and efficiency of the FVM are comparable to those of the FDM.