适用于混合网格的约束最小二乘重构方法

 为强化边界条件对计算流体力学(CFD)计算中流场重构过程的影响,基于三维任意多面体混合网格,对一种约束最小二乘法进行了研究。通过对不同边界类型的透明化处理,统一了约束方程组的形式,从而简化了该方法的应用。为了充分吸收消去法和加权法各自求解约束方程组的优点,提出了混合采用两种方法的思路。针对层流平板研究了加权法中加权系数如何取值问题,数值实验表明加权系数取到5基本已经足够大。最后通过亚声速层流平板和跨声速湍流ONERA-M6算例对比了混合法、加权法与原始最小二乘法,计算结果表明:约束最小二乘法相比原始最小二乘法的流场重构更加准确,特别是对边界质量较差网格的计算优势更为突出;混合消去加权法相比单独采用加权法的计算结果也有所改善。

Constrained Least-squares Reconstruction Method for Mixed Grids

In order to enforce the effect of boundary conditions on the solution reconstruction of computational fluid dynamics(CFD) simulation,a constrained least-squares method based on arbitrary polyhedral mixed grids is investigated.To make the method simpler,a uniform constrained system is constructed through treating different boundary conditions in the same way.To make use of the advantages of both the elimination approach and the weighting approach,a mixed method is provided to solve the constrained system.The numerical experiments based on laminar plates show that setting the weighting coefficient to 5 is large enough in the weighting approach.The numerical results of a subsonic laminar flow over a plate and a transonic turbulent flow over ONERA-M6 demonstrate that the constrained least-squares method is more accurate than the original least-squares method,especially when bad quality grids are used near the boundary,and that the mixed method shows improved results as compared with the weighting approach.