基于代数变分多尺度—多重网格高精度混合算法的叶轮机械非定常数值模拟研究

The project focuses on high accuracy and high resolution algorithm. The construction of high order accuracy hybrid schemes is started from numerical research of model equations, and combined with algebraic multiscale-multigrid algorithm and wavelet multiscale-multigrid algorithm to enhance the calculation speed, the calculation stability, and so on. By comparing different calculation programs, we tried to conduct a comprehensive analysis and evaluation for numerical methods. The stability and efficiency of the method are verified based on the numerical calculation of the inviscid Euler equations. By comparing different DES models, we chose the ideal DES turbulence model. Finally, by using an ideal high accuracy algorithm and the appropriate DES model, high accuracy simulation platform of turbomachinery internal flow is developed to realize the accurate numerical simulation of turbomachinery complex flow.

本项目重点研究高精度、高分辨率数值方法。从模型方程数值研究入手，构造高精度混合计算格式，在此基础上，结合代数多尺度—多重网格算法和小波多尺度—多重网格算法，增强算法的计算速度和稳定性。通过不同计算程序的研究，对数值方法进行全面的分析和评价；基于无粘Euler方程的数值计算，验证此方法的稳定性和计算效率。最后，利用较优的高精度计算方法，开发出叶轮机械内部流场高精度数值模拟平台，以实现叶轮机械内部复杂流场准确的数值模拟。

本项目着眼于高精度WENO类格式研究，重点研究了简单限制器的WENO5有限体积格式、Hermite WENO DG/FV混合格式及紧致型WENO格式。结合代数多重网格算法，增强了原高精度计算程序的计算速度和稳定性。通过不同计算程序的研究，对上述三种WENO类数值方法进行了全面的分析和评价；基于无粘Euler方程的数值计算，验证了简单限制器的WENO格式的稳定性和计算效率。利用较优的简单限制器的WENO格式，开发出叶轮机械内部流场高精度数值模拟平台，实现了叶轮机械内部复杂流场高精度数值模拟。