拉氏流体动力学中基于多物理量的沙漏算法研究

拉氏流体动力学是多物理、多介质流体力学数值模拟中的重要工具之一,其在武器物理、飞行器设计、汽车安全性能评估、天文现象数值模拟等众多领域有着广阔的应用。拉氏方法中的一个关键问题就是如何有效的控制计算网格在模拟过程中的非物理扭曲和大变形。沙漏畸变就是其中一类重要的非物理变形。本项目针对交错型拉氏方法中的沙漏变形问题，致力于发展基于多物理量的新型沙漏控制算法。该算法将充分利用流体的有效物理信息，构造出更加有效的反沙漏力，既能有效的抑制网格的虚假运动，又能避免对数值解添加过多的人工刚性；研究沙漏控制算法和数值人工粘性关系，促进两类方法有效合作，同时给出合适的沙漏系数和粘性系数；最终发展相应的低参数依赖的具有强健壮性、高置信度的交错型拉氏方法。本项目研究的是拉氏流体动力学模拟中的难点问题，将显著的提高拉氏数值模拟的可靠性和有效性，所提出的算法将应用于实际的物理问题中。

The Lagrangian hydrodynamics plays an important role in the multi-physics and multi-material computational fluid dynamic simulations. The Lagrangian method has a wide range of applications in weapon physics, aircraft design, automobile crashworthiness evaluation, and astrophysical simulation. An essential problem in Lagrangian simulation is the non-physical mesh tangling and large deformation, especially the hourglass instabilities. This project will focus on the hourglass distortion in staggered Lagrangian hydrodynamics. We intend to develop a novel multi-physics based hourglass control algorithm, the proposed hourglass algorithm will coupling the information of various physical variables of the fluids to construct the effectively perturbed anti-hourglass force, it can effectively suppress the spurious grid motion, meanwhile, avoid adding too much numerical stiffness to the solution; we will investigate the internal connection between the hourglass control algorithm and the artificial viscosity and promoting the collaboration of the two approaches, simultaneously giving the proper parameters for the hourglass control and the artificial viscosity; eventually, improve the robustness and the believability of the Lagrangian simulation. This project focuses on the key problem of Lagrangian hydrodynamics and will lead to a remarkable improvement of the reliability and the efficiency of the Lagrangian simulation. The algorithm can be further applied to the real data problem.