跨音速有旋流动正问题的赝势函数变分有限元法

本文运用赝势函数变分有限元方法数值模拟了绕翼型的跨音速有旋流动。在含有激波的跨音速有旋流动中，势函数已不存在，但为了保留势函数模型在求解方面的优越性，上海大学的刘高联引入了一个通用函数一赝势函数，可以看出该赝势函数保持了势函数的所有好处，又突破了流动有势的限制，是势函数对有旋流动的一个自然的、物理上相容、数学上求解简便的推广，进一步地，刘高联还得到了赝势函数的变分原理族，为变分有限元法求解有旋流动打下了基础。另一方面，为了提高数值求解的收敛性和有效地捕捉流场中的激波，本文还采用了“人工密度”办法。绕翼型的跨音速有旋流动的计算实践证明了赝势函数的有效性。

Variation FEM for Direct Problem of Transonic Rotational Flow Using Pseudo-potential Function

The variation finite element method(FEM) using the pseudo-potential function was presented for the simulation of transonic rotational flows. As known, there isn't potential function in the transonic rotational flows with shock waves. But in order to preserve the computational simplicity of the potential function, one general function-the pseudo-potential function-was introduced by Liu Gao-Lian of Shang-Hai University. Liu has shown that the pseudo-potential function retains almost all advantages of potential function and removes its restriction to flow potentiality, while providing a new physically self-consistent and computationally simple flow potentiality, while providing a new physically self-consistent and computationally simple flow model and allowing for the vorticity generated just behind shocks. Moreover, a family of variational principles for the pseudo-potential function was also established by Liu. On the other hand, the artificial density approach was implemented in this paper to improve the solution convergence and to capture the shocks effectively. The reasonable and satisfied results presented showed that the current method is effective and robust for simulation of transonic rotational flows.