A Blended Continuation Method for Solving Steady Inviscid Flow

一种求解定常无黏流场的混合延拓方法

¹ Northwestern Polytechnical University, School of Aeronautics, Xi'an 710072, China
² China Aeronautical Establishment, Aviation Industry Corporation of China, Beijing 100012, China

Received: 7 March 2017

Abstract

Steady flow field solving is wieldly used in aircraft aerodynamic design, efficiency of steady flow field solving has great influnence on efficiency of aircraft aerodynamic design. A continuation method that blended Laplacian operator and pseudo time marching method for solving steady inviscid flow problem is proposed. In steady flow problem, the field is usually initialized as an uniform field before starting iteration. This resulted in the fact that the initial residual in only nonzero on wall boundary. Based on this feature, Laplacian operator is introduced to accelarate convergence at the starting stage of nonlinear solving. At the ending stage of nonlinear solving, the blended continuation term is biased to pseduo time marching method to avoid over dissipation graduately. To establish a complete continuation method, the starting, evolution and termination method are also described. At last, the proposed continuation method is implemented in a finite element solver, and tested aginst GAMM channel and NACA0012 foil subsonic and transonic cases. Numerical test results confirmed that the blended continuation method could get an efficency improvement about 1/3 to 1/4 comparing with stand alone Laplacian continuation and much more better than pure pseudo time marching method.

摘要

定常流场的求解在现代飞行器气动设计中有着广泛的应用，流场求解效率对飞行器优化的效率有着重要影响。提出了一种将拉普拉斯（Laplace）算子与伪时间推进法相结合的混合方程延拓方法，用于求解定常无黏流动问题。在定常流动问题中，流场通常被初始化为均匀来流条件，然后再开始迭代求解。这就导致初始残差仅在靠近边界的网格处不为零。针对这一特点，通过拉普拉斯算子作为额外耗散措施，加速非线性迭代在求解初期的收敛速度。在非线性迭代的后期，为避免拉普拉斯算子的过度耗散，混合延拓方法逐步过渡为由伪时间项主导。为构造完整的非线性迭代策略，同时给出了延拓系数的初始化、递推和终止方法。最后，将所构造的方法应用于有限元欧拉方程求解器中，分别通过GAMM鼓包内流算例和NACA0012外流算例，在亚声速和跨声速条件下对计算效率进行了验证。数值实验结果表明，混合延拓方法在跨声速算例中可以比单纯拉普拉斯延拓提高1/3~1/4收敛速度，相对于单纯时间推进法的效率提升更为显著。