非结构网格迎风格式中的一种重构方法研究

A New Way of Determining Nodal Quantities for Upwind Schemes on Unstructured Meshes

研究了一种基于网格节点重构的二阶迎风格式在非结构网格无粘流场计算中的应用 ,提出了一种新的网格节点流场参数的重构方法。并通过 ONERA M6机翼、带副翼的直机翼、翼身组合体以及翼身组合体带增升装置无粘绕流流动计算对该重构方法进行了验证。算例表明新方法可以在确保格式精度和不显著增加流场计算时间的前提下 ,明显改善迎风格式的稳定性、收敛性和鲁棒性 ,减小了网格质量对流场求解精度的影响 。

Refs.1 through 4 employed with considerable success the second order upwind scheme proposed by N.T.Frink but their ways of determining nodal quantities meet, in our opinion, with much trouble in such cases like gap flow and viscous flow. We, therefore, after much research, propose a new way of determining nodal quantities. Taylor expansion shows the existence of the relationship: q j=q i+ q x i(x j-x i)+ q y i(y j-y i)+ q z i(z j-z i)+O( Δ r 2), (j=1,2,…,N). The three unknown quantities,  q x i,  q y i,  q z i, can be solved from ( N-1 ) linear algebraic equations. Then the typical nodal quantity q 0 can be determined from the following equation: q 0=q i+ q x i(x 0-x i)+ q y i(y 0-y i)+ q z i(z 0-z i). The developed method was used to simulate four flows around: (1) the ONERA M6 wing, (2) an unswept wing with a half span flap, (3) wing body configuration, (4) wing body with high lift configuration. The results, as given in Table 1 and Figs.6 through 10, indicate that not only the iterative number can be reduced but also the stability, convergence and robustness of upwind scheme can be remarkably increased. By using the scheme presented in this paper, the influence of mesh quality on accuracy can be greatly decreased; so it is particularly useful in handling flow problems around complex configurations with unstructured meshes.