基于局部无网格的混合算法研究

A new type hybrid algorithm using local gridless techniques

研究了一种求解任意外形绕流的局部无网格混合算法。该算法计算区域整体采用了直角网格,只在物面附近嵌入局部无网格处理。整体直角网格的规则性与正交性,不仅使得网格生成快,而且计算格式实施简单,避免了与非正交性相关的计算项,从而引入误差相对较小。局部无网格处理只要求物面附近布点离散,具有灵活性,使得发展的算法适合处理任意外形。先以理想不可压流动问题为例,给出了其控制方程Laplace方程的具体求解实施过程,并给出了直槽道内柱体绕流的计算结果;接着把方法推广用于求解可压缩流动的Euler方程,对喷管等典型流动问题进行了数值模拟,并与传统有限体积法结果进行了比较,在捕捉的波系结构、表面压力系数分布等方面具有良好的一致性,表明发展的新方法是可行的。

A new type hybrid algorithm using local gridless techniques （HLG） is developed for the solution of flows over arbitrary configurations. In this approach, the flow field is basiclly discretized by Cartesian grids, and local gridless treatment is embedded in the regions adjacent to bodies. Because of Cartesian mesh＇ s regularity and orthogonality, it not only provides an efficient mesh generation with simple implementation of numerical schemes, but also eliminates issues associated with mesh skewness and distortion, which offers the advantage of shock capturing with minimal phase error. Furthermore, local gridless techniques only require a few of points be distributed in the regions adjacent to the bodies, and so the proposed algorithm with this flexibility is well suited to arbitrary configurations. Begin with a case of ideal incompressible flow, the procedure to solve the Laplace equation as the governing equation is described in details, and the solution for flows around cylinders in rectangular channel is presented. Then, the new hybrid algorithm is further developed for solving compressible Euler equations. Identical problems such as flows across channels are numerically simulated, and comparison with traditional finite volume method （FVM） is presented .Good agreement of the captured shock waves and surface＇s pressure coefficients is observed, and the validity of the proposed new method is demonstrated.