关键词: 跨音速流, 欧拉方程, 数值计算

Abstract:

The Euler equations of the two-dimensional transonic flow around airfoils are solved by the finitevolume method with Mac-Cormack explicit scheme, The boundary conditions on the airfoil surface are derived directly using the momentum equations on the mesh cell in the present paper. The new conditions are of the same two-order accuracy with the difference formulas in the flow field, and avoid to computing numerically the coordinate derivatives, which generally have the large errors. The no-reflected far-field conditions are used as well. The convergence rates are effectively improved when the enthalpy damping is included. According to the multigrid principle, an explicit multigrid scheme is devised to accelerate the convergence of the calculations of Euler equations. The four-level multigrid algorithm is used, and the convergence processes are dramatically changed. The satisfied results of the typical transonic flows on NACA0012 airfoil are obtained.

Key words: transonic flow, Euler equation, numerical calculation