关键词: 非线性方程, 隐式格式, 牛顿法, 空气动力学, 跨声速, 定常流动

Abstract: The implicit solving approach of steady transonic flow field equals a Newton iteration for a nonlinear equation system. Globalization of Newton iteration is usually necessary in practice in order to fulfill the convergence requirement. In the framework of homogenous continuation, a Laplace operator based function continuation method which accelerates convergence of implicit solving of steady flow field is proposed. Considering that the steady flow field is usually initialized as uniform freestream condition, the Laplace operator is employed to speed up information propagation from wall boundary to internal flow field due to its ellipticity and to improve regularity of the problem due to its linearity and symmetric positive definite property. Thus the stability of Newton's method is improved then larger CFL number could be employed and finally the flow field solving efficiency is improved. Due to the complexity and nonlinearity of the flow field problem, a priori optimal nonlinear solving strategy is impossible to be obtained through theoretical analysis. Thus, the effect of Laplacian coefficient on convergence efficiency is investigated through numerical experiments on inviscid NACA0012 airfoil, turbulent RAE2822 airfoil and ONERA M6 3D wing test cases. Generally pragmatic combination of iteration parameters are also given and the proposed method is proved to gain over 20% saving in CPU computing time compared with the classic pseudo time marching method under transonic condition.

Key words: nonlinear equations, implicit scheme, Newton's method, aerodynamics, transonic, steady flow