流体中普适的黎曼解法器求解方法

Method of the Riemann Solver and Application in Fluids

研究了一种普适流体力学的准确黎曼解法器求解方法,该方法可以应用于纯流体、两相流以及弹塑性流体.利用特征理论分析流体力学的连续偏微分方程组系统的双曲性,由特征值得到黎曼解法器的完整波系结构,从右特征向量建立满足完整波系的间断关系式来封闭求解得到黎曼解法器.该解法器具有完整波系结构,且包含原连续系统数学性质,能准确得到跨过不同波的物理量.在应用到拉氏方法或ALE方法中计算多介质问题时,由迎风性确定线性退化波两侧的物理量精度高,数值耗散性小,可以提高格式的精度.文中分别给出两相流和弹塑性流的数值算例,结果均显示了解法器的优点和特性.

A method of the exact Riemann solver was studied to be widely used in multi-fluids,such as pure fluid,non-conservative two phase fluids,as well as the elastic-plastic flows.Firstly,the continuous hyperbolic character of hydro-mechanical partial differential eguation was analyzed based on the characteristic theory.Then,the full wave structure of the Riemann solver was obtained from its right characteristic values.Finally,a disconnected relation formula of the full wave system was developed to establish the Riemann solver automatically.Results show that,the Riemann solver possesses full wave structure of the Riemann problem,includes all mathematics properties of the continuous system,and can obtain the exact physical values across the waves.When it is used in the Lagrangian method or the ALE ones to solve the multi-material problems,the Riemann solver obtains the exact values from the coming wind,shows a high accuracy and less dissipation.Numerical experiments in two-phase flows or the elastic-plastic flows validate the merits and characteristics of the Riemann solver.