多介质弹塑性流体力学多维Riemann解法器研究

Multimaterial elastic-plastic flows are common media in the study of weapon physics and Inertial Confinement Fusion (ICF), where large interface deformation, high density ratio and high pressure ratio are encountered frequently. Low resolution, numerical instability and interface treatment are common diffculties faced in modeling and simulating multimaterial/multicomponents flows. Such diffculties are found to be even worse and more chanllenging in the simulation of multimaterial elastic-plastic flows. Evidences showed that such worse phenomena are someway related to the neglect of multidimensionality in the approximation of Riemann problem in high dimensions. Up to date, there is barely research work taking into account the multidimensionality of Riemann problem in high dimensions. Based on our experience and research in the study of multimaterial Riemann problems, we plan to develop new approximate Riemann problem solvers with the consideration of multidimensionality effect. We expect to provide solution to suppress the numerical instability encountered in the current centered Lagrangian and ALE methods when applied to simulate multimaterial elastic-plastic flows. Through the study of this project to be proposed, we may develop new techniques with a sound basis to promote the quality and credibility of numerical results.

在武器物理和惯性约束聚变（ICF）等领域的研究中都遇到大变形、高密度比、高压力比的多介质弹塑性流体。流场分辨率不高、计算不稳定和物质界面难以处理等是模拟可压缩多介质流遇到的共性问题。这些问题在模拟武器物理的多介质弹塑性流体时变得更加恶化和严重。这些现象在一定程度上都和没有考虑 Riemann 问题解的多维效应有关。然而针对多介质弹塑性流体力学的多维Riemann问题解法器的研究目前国内外还是空白。基于在多介质Riemann问题研究方面多年的经验和成果，项目申请团队计划研究多介质弹塑性流体二维Riemann问题解法器，并以此为基础解决困扰目前二维中心型拉格朗日和ALE方法的数值不稳定性等方面的问题。通过此项研究，我们希望能够为目前武器物理和ICF研究中的一些算法构造及数值模拟瓶颈问题的解决提供新的思路和理论支撑，并以此提升对这些挑战性问题数值模拟的准确性。

在武器物理和惯性约束聚变（ICF）等工程应用领域中，爆轰、冲击等因素作用常常会诱导多介质弹塑性流体的相互作用，产生复杂的固体变形以及应力波传播、反射及相互作用。弹塑性流体的数值算法，尤其是多维弹塑性黎曼解法器，可被看成认识弹塑性流体物理特性的重要工具。针对此，联合团队探索了多维弹塑性黎曼解理论，发展了基于不同弹塑性方程形式的（欧拉、拉格朗日和任意欧拉拉格朗日）弹塑性流体计算方法，开发了高置信度的弹塑性黎曼解程序模块。并针对多介质弹塑性流体力学数值模拟的实际需求，把相关理论成果以模块形式应用到北京应用物理与计算数学研究所相应的程序中，解决了弹塑性算子分裂算法精度不足的问题，拓展了工程应用ALE程序的应用范围。通过此项研究，我们为目前武器物理和ICF研究中的一些算法构造及数值模拟瓶颈问题的解决提供了新的思路和理论支撑，并以此提升了对这些挑战性问题数值模拟的准确性。

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