充液容器大幅晃动问题的三维物质点有限元法研究

Large-amplitude liquid sloshing in containers is of great concern to many disciplines and engineering fields. Sloshing processes involve the complex variation of liquid surface as well as the strong coupling between the fluid and the walls of the container, which bring many difficulties to numerical simulation. Newly-emerged material point method (MPM) possesses the advantages of both Lagrangian and Eulerian descriptions, so MPM can deal with moving interfaces and large material deformation easily, and it is much suitable for solving fluid-structure interaction (FSI) problems. With large-amplitude liquid sloshing problems as the background, the three-dimensional material point finite element method for strong FSI problems will be developed in this project. Firstly the MPM direct solution scheme for incompressible flow problems. The new scheme can overcome the disadvantages of current weak-compressiblity scheme. The treatment of free surface will also be improved. Then the material point-shell/plate finite element coupling method will be constructed. The fluid region will be simulated by MPM, and the solid region will be simulated by shell/plate elements, and a seamless coupling solution will be developed for large-amplitude sloshing problems. Next, a multiple-time-step integration scheme for the coupling method will be presented, so that matching will be achieved for time step sizes of different regions. Finally, three-dimensional material point-finite element program FEMP3D for strong FSI problems will be studied and developed. The sloshing experiments of typical liquid containers will be carried out as well. The FEMP3D program will be verified and validated, and it will be applied into sloshing problems of typical liquid containers. The research achievements are of great theoretical value, and they have important application prospect in many engineering areas.

充液容器中液体的大幅晃动是多个学科和工程领域中的重要问题。晃动过程中液面变化非常复杂，液固耦合作用很强，给数值分析带来了很多困难。近年来新兴的物质点法兼具拉格朗日和欧拉描述的优点，易于处理移动界面和物质超大变形，非常适合求解流固耦合问题。本项目以充液容器大幅晃动问题为背景，发展强流固耦合问题的三维物质点有限元法。首先建立不可压缩流问题的物质点直接求解方案，以解决现有弱可压求解方案的缺点，并改进物质点法中自由液面的处理方式；然后建立物质点-板壳有限元耦合方法，用物质点法模拟流体区域、板壳单元模拟固体区域，实现大幅晃动问题的无缝耦合求解；之后发展耦合方法的多时间步长积分方案，达到不同区域的时间步长匹配；最后研制强流固耦合问题的三维物质点有限元法程序FEMP3D，同时进行典型充液容器晃动实验，对程序进行验证与确认，并将其应用于典型液舱晃动问题中。本项目的研究成果具有重要的理论意义和应用前景。

充液容器中液体的大幅晃动是多个学科和工程领域中的重要问题。晃动过程中液面变化复杂，液固耦合作用强，给数值分析带来了诸多困难。近年来新兴的物质点法兼具拉格朗日和欧拉描述的优点，易于处理移动界面和物质超大变形，非常适合求解流固耦合问题，但标准物质点法在求解长物理时间流动和流固耦合问题时计算量很大。本项目以充液容器大幅晃动问题为背景，发展了强流固耦合问题的三维物质点有限元法。建立了不可压物质点法，解决了现有弱可压求解方案的缺点，可很好地模拟液体流动问题；改进了物质点法中自由液面的处理方式，对卷曲、破碎、融合等复杂液面变化过程具有较好的模拟精度，非常适于自由液面流动问题的求解；建立了物质点-板壳有限元耦合方法，用物质点法模拟流体区域、板壳单元模拟固体区域，实现不同区域的无缝耦合求解；将上述成果集成到大型三维物质点法程序MPM3D，通过典型自由液面流动和液固耦合实验结果进行了多方验证，成功应用于强流固耦合问题。本项目的研究成果为充液容器大幅晃动等强流固耦合问题提供了新型数值分析手段，具有重要的理论意义和应用前景。