多重网格法求二元跨声速流在一种半自适应网格上的欧拉解

STEADY SOLUTIONS OF TRANSONIC EULER FLOWS ON SEMI-SELF-ADAPTIVE MESHES BY MULTIGRID METHOD

本文采用MacCormack两步显式格式,用有限体积法求解了二元跨声速欧拉流。推导了物面边界条件,采用了特征远场边界条件及远场环量修正。利用保角变换方法生成O型贴体网格,并修改得到了一种在激波处局部加密的半自适应贴体网格。采用多重网格及焓阻尼加速收敛技术计算了NACA0012翼型的跨声速气动特性,得到了十分满意的收敛过程和计算结果。

The Euler equations of the two-dimensional transonic steady flow around airfoils are solved by the finite-volume method with MacCormack explicit scheme. The boundary conditions on the airfoil surface are treated directly using the momentum equations on the boundary mesh cell and the non-reflected far-field conditions with circulation corrections a're used. An O-type body fitted grid is generated by using the Joukowsky mapping function with some modifications of the meshes near the body surface. The generations are simple and fast. The semi-self-adaptive meshes which are dense in the neighbourhood of the shock wave are generated. The enthalpy damping is included and a 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 accelerated significantly. Satisfactory results of the typical transonic flows past NACA 0012 airfoil are obtained.