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 引用本文: 刘溢浪, 张伟伟, 蒋跃文, 叶正寅. 一种基于增量径向基函数插值的流场重构方法[J]. 力学学报, 2014, 46(5): 694-702.
Liu Yilang, Zhang Weiwei, Jiang Yuewen, Ye Zhengyin. A RECONSTRUCTION METHOD FOR FINITE VOLUME FLOW FIELD SOLVING BASED ON INCREMENTAL RADIAL BASIS FUNCTIONS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(5): 694-702.
 Citation: Liu Yilang, Zhang Weiwei, Jiang Yuewen, Ye Zhengyin. A RECONSTRUCTION METHOD FOR FINITE VOLUME FLOW FIELD SOLVING BASED ON INCREMENTAL RADIAL BASIS FUNCTIONS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(5): 694-702.

## A RECONSTRUCTION METHOD FOR FINITE VOLUME FLOW FIELD SOLVING BASED ON INCREMENTAL RADIAL BASIS FUNCTIONS

• 摘要: 由于流场参数重构中， 用于重构的基网格单元的物理参数波动量相对于均值较小， 径向基函数（RBF） 直接插值方法重构会产生较大的数值振荡， 论文提出了一种增量RBF 插值方法， 并用于有限体积的流场重构步， 明显改善了插值格式的收敛性和稳定性. 算例首先通过简单的一维模型说明该方法的有效性， 当目标函数波动量相对于均值为小量时， 增量RBF 插值能够抑制数值振荡； 进一步通过二维亚音速、跨音速定常无黏算例、静止圆柱绕流非定常算例以及超音速前台阶算例来说明该方法在典型流场数值求解中的通用性和有效性. 研究表明增量RBF 重构方法可陡峭地捕捉激波间断， 可有效改善流场求解的收敛性和稳定性， 数值耗散小， 计算效率高.

Abstract: A reconstruction method of flow field solving, based on incremental RBF (Radial Basis Functions) interpolation, has been developed in the paper. Since the fluctuation of flow parameters in the stencil cells used to reconstruct is small compared with the mean value in flow field reconstruction, direct RBF reconstruction will bring large numerical oscillations. The incremental RBF reconstruction developed in this paper effectively improves convergence and stability of the interpolation scheme. In first example, a simple one-dimensional model is used to illustrate the effective of this method when the fluctuation of the objective function is much smaller than the mean value. Furthermore, applicability and effectiveness of incremental RBF reconstruction method is proved by using four typical flow fields, namely, two-dimensional subsonic, transonic inviscid steady flow fields around NACA0012, the viscid unsteady flow around a stationary cylinder and a Mach 3 wind tunnel case with a step problem. Research shows that incremental RBF reconstruction method can smoothly capture steep shock and effectively improve the convergence and stability of flow solver with small numerical dissipation and high computational efficiency.

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