论文部分内容阅读
DG/FV混合方法因其具有紧致、易于推广获得高阶格式及相比同阶精度DG方法计算量、存储量小等优点,自提出以来已成功应用于一维、二维标量方程和Euler/N-S方程的求解。综述了DG/FV混合方法的研究进展,重点介绍了DG/FV混合方法的空间重构算法、针对RANS方程的求解方法、隐式时间离散格式、数值色散耗散及稳定性分析、计算量理论分析,并给出了系列粘性流算例的计算结果,包括用于验证混合方法数值精度的库埃特流,以及方腔流、亚声速剪切层、低速平板湍流、NACA0012翼型湍流绕流等。数值计算结果表明DG/FV混合方法达到了设计的精度阶,且相比同阶DG方法计算量减少约40%,而隐式方法能大幅提高定常流的收敛历程,较显式Runge-Kutta的收敛速度提高1~2个量级。
The DG / FV hybrid method has been successfully applied to one-dimensional and two-dimensional scalar equations and Euler since its introduction because of its compactness, easy generalization of high-order formats, and its advantages compared with the same-precision DG method. / NS equation to solve. The research progress of DG / FV hybrid method is reviewed. The spatial reconstruction algorithm of DG / FV hybrid method is emphatically introduced. According to the solving method of RANS equation, implicit time discrete format, numerical dispersion dissipation and stability analysis, The calculation results of the series of viscous flow cases are given, including the Kurt’s flow used to verify the numerical accuracy of the mixing method, as well as the square cavity flow, subsonic shear layer, low-velocity plate turbulence, NACA0012 airfoil turbulent flow Wait. The numerical results show that the DG / FV hybrid method achieves the accuracy of the design, and the computational complexity is reduced by about 40% compared with the DG method of the same order. The implicit method can greatly improve the convergence of the steady flow. Compared with the explicit Runge-Kutta Convergence rate increased by 1 to 2 orders of magnitude.