谱体积方法单元分割与问题单元标记方法的改进研究

谱体积方法是一种本质上解决网格依赖性的高精度CFD计算方法,本文研究了二维Euler方程的谱体积方法,提出一种基于切比雪夫多项式的单元分割方法,建立了基于WENO的变量限制器方法,并发展了结合谱体积和控制体的问题单元标记方法.采用15°超声速压缩拐角和NACA0012跨声速流动两个典型算例进行验证,结果表明,该分区方法具有更好的计算精度,标记方法可有效识别不连续区域,在较少的网格下即可获得与密网格传统有限体积法相当的计算精度.

A study on the cell partition and trouble cell marking method of spectral volume method

The spectral volume method is a high-precision CFD calculation method that essentially resolves the grid dependence.This paper is mainly focused on the spectral volume method of the two-dimensional compressible Euler equation.A new cell partition method is proposed based on the Chebyshev polynomial, and a WENO-based Variable limiter method is established to develop the trouble cells marking method combined with the spectral volume and control volume.Two typical numerical examples of 15° supersonic compression wedge and NACA0012 transonic flow are used to do the verification.The results indicate that the new partitioning method has better accuracy compared with existing methods, and the marking method can effectively identify discontinuous areas.Finally, the SV method with a coarse grid can achieve accurate results equivalent to the common finite volume method under fine grids.