面向可压缩激波流动的数值方法研究

Shock-fitting technique has been used to solve compressible flows with shock waves at the dawn of CFD for it can present an exact solution. But when be used in complex flows, it is difficult to apply for many manual intervention. With the development of shock-capturing schemes, its large automation makes it more popular than the shock-fitting. However, the shock-capturing schemes, which is proven to be of high accuracy has only first order in the vicinity of shock waves..In the previous research, we applied the idea of shock-fitting into a unstructured dynamic grids solver which is based on shock-capturing algorithms, and proposed a simple computational method which is called “unstructured boundary fitting solver, UBFs”. This method greatly improves the ability of shock-fitting assembly to deal with complex flows. On the base of former studies, we are planning to put forward a new shock-fitting method in order to improve its ability in being used in practical engineering. And then a related shock detection technique will be researched to improve the automation of shock-fitting. Finally, a full field high accuracy method will be established which is base on the new shock-fitting method and the research results of high precision shock-capturing schemes.

激波装配方法因能精确求解激波，在计算流体力学发展初期就被用来处理含有激波的可压缩流动，但在处理复杂激波流动时，其应用过程较为复杂，难以建立统一的求解程序，逐渐被自动化程度较高的激波捕捉方法所取代。而在光滑区域性能表现优良的高精度捕捉算法在激波区域被证实只有一阶精度。.在前期研究中，我们将激波装配精确求解激波的思想应用到基于捕捉算法的非结构动网格求解器中，发展出非结构边界激波装配方法，去除了结构网格的拓扑限制，大大提高了激波装配方法对复杂流动的处理能力。本项目拟在前期研究的基础上，发展新型激波装配方法，改善传统装配方法难以实际应用的窘况；然后研究与之相关的激波辨识技术，建立快速识别激波变化的手段，提高激波装配的自动化程度；最后以新型激波装配方法为基础，结合目前高精度捕捉格式的诸多研究成果，建立具有全场一致高精度特点的超声速流动计算方法，提高目前超声速，特别是高超声速流动的数值计算水平。

本课题以超/高超声速可压缩流场中的激波作为研究对象，在课题组已有的边界激波装配法和嵌入式激波装配法的基础上，发展了一种可适用于非定常流场计算的自适应间断装配方法。自适应间断装配方法以高精度的激波探测技术为基础，通过激波探测技术确定流场中激波结构所在网格节点后，再通过流场初始化、间断节点物理量修正、网格节点运动及流场更新等四个过程进行求解。其中，激波探测技术通过引入K-means聚类算法分片拟合出了高质量的激波线/面，与传统方法相比其精度及可靠性都有了很大提升。自适应间断装配法能够统一处理边界激波和内嵌激波，极大地提高了计算效率。此外，自适应间断装配法通过特殊处理间断节点沿壁面的运动、自动重构间断节点分布及间断附近网格分布等策略提升了对非定常问题的处理能力，尤其是对含有大位移或大变形激波的非定常流场。在实现对流场中激波的精确计算后，结合现有的高精度激波捕捉算法及本课题提出的边界算法可实现对流场全场不低于二阶精度的计算。该边界算法是一种部分隐式的梯度重构方法，通过在边界变量重构过程中引入边界约束而实现，同时使用对边界附近的隐式线性系统迭代求解、引入矢量型的梯度限制器等策略大大提高了该方法的鲁棒性