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姚成宝, 付梅艳, 韩峰, 闫凯. 欧拉坐标系下具有锐利相界面的可压缩多介质流动数值方法研究[J]. 力学学报, 2020, 52(4): 1063-1079. DOI: 10.6052/0459-1879-20-054
引用本文: 姚成宝, 付梅艳, 韩峰, 闫凯. 欧拉坐标系下具有锐利相界面的可压缩多介质流动数值方法研究[J]. 力学学报, 2020, 52(4): 1063-1079. DOI: 10.6052/0459-1879-20-054
Yao Chengbao, Fu Meiyan, Han Feng, Yan Kai. NUMERICAL SCHEME OF MULTI-MATERIAL COMPRESSIBLE FLOW WITH SHARP INTERFACE ON EULERIAN GRIDS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(4): 1063-1079. DOI: 10.6052/0459-1879-20-054
Citation: Yao Chengbao, Fu Meiyan, Han Feng, Yan Kai. NUMERICAL SCHEME OF MULTI-MATERIAL COMPRESSIBLE FLOW WITH SHARP INTERFACE ON EULERIAN GRIDS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(4): 1063-1079. DOI: 10.6052/0459-1879-20-054

欧拉坐标系下具有锐利相界面的可压缩多介质流动数值方法研究

NUMERICAL SCHEME OF MULTI-MATERIAL COMPRESSIBLE FLOW WITH SHARP INTERFACE ON EULERIAN GRIDS

  • 摘要: 可压缩多介质流动问题的数值模拟在国防和工业领域内均具有重要的研究价值,诸如武器设计、爆炸安全防护等,通常具有大变形、高度非线性等特点,是一项极具挑战性的研究课题. 本文提出了一种基于 Euler 坐标系的非结构网格、具有锐利相界面的二维和三维守恒型多介质流动数值方法,可用于模拟可压缩流体和弹塑性固体在极端物理条件下的大变形动力学行为. 利用分片线性的水平集函数重构出单纯形网格内分段线性的相界面,并在混合网格内构建出具有多种介质的相界面几何结构,理论上可以处理全局任意种介质、局部 3 种介质的多介质流动问题. 利用传统的有限体积格式来计算单元边界上同种介质间的数值通量,并通过在相界面法向上求解局部一维多介质 Riemann 问题的精确解来计算不同介质间的数值通量,保证了相界面上的通量守恒. 提出了一种非结构网格上的单元聚合算法,消除了由于网格被相界面分割成较小碎片、违反 CFL 条件,进而可能带来数值不稳定的问题. 针对一维多介质 Riemann 问题、激波与气泡相互作用问题、浅埋爆炸问题、空中强爆炸冲击波和典型坑道内冲击波传播问题开展了数值模拟研究,将计算结果与相关的理论、实验结果进行比对,验证了数值方法的正确性和可靠性.

     

    Abstract: Numerical simulation of multi-material compressible flow problem is of great importance in both the national defense and industry areas, such as weapon design and blast wave defense. Due to the property of large deformation and high nonlinearity, the efficient simulation of multi-material compressible flow becomes a quite challenging problem. A numerical scheme is developed to carry out the simulation of an immiscible multi-material compressible flow with sharp phase interface on two dimensional and three dimensional unstructured Eulerian grids, which can handle the large deformation of compressible fluid and elastoplastic solid under the extreme conditions. We use the level set method to depict the phase interface numerically, and explicitly reconstruct the phase interface in a piecewise linear manifold. The topological structure of the phase interface is constructed explicitly, which can handle any number of media in the whole computational domain and three media in a single cell. The traditional finite volume method is used to calculate the edge numeircal flux between the same material in adjacent cells, while the phase interface flux is calculated by exactly solving a one dimensional multi-material Riemann problem on the normal direction of the phase interface. The above procedures can keep the conservation of the phase interface flux, and the interaction between two media across the phase interface can keep consistent with the real situation. A robust aggregation algorithm is adopted to build cell patches and adjust the conservation variables around the phase interface, which can effectively remove the numerical instability due to the breakdown of the CFL constraint by the cell fragments. Some classical examples and application problems, such as one-dimensional multi-material Riemann problem, gas-bubble interaction problem, intensive airblast problem, sub-surface blast problem, and blast wave propagation in three dimensional sap, which have a good agreement with the corresponding analytical and experimental results, are presented to validate our numerical scheme.

     

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