流固耦合不可压物质点法及其在晃动问题中的应用

Fluid structure interaction incompressible material point method and its applications in sloshing problem

作为一种混合拉格朗日欧拉法,物质点法在流固耦合问题中具有重要的应用前景。对于自由液面的流动问题,基于物质点法框架已建立了弱可压物质点法和完全不可压物质点法,但在处理流固耦合问题时遇到了困难。弱可压物质点法由于采用可压缩状态方程,导致求解时间步长过小,压力振荡严重,产生了非物理的飞溅现象;完全不可压物质点法基于投影算法和不可压条件,消除了弱可压物质点法的压力振荡,提高了时间步长,但难以处理移动边界问题。基于变分形式的投影算法提出了一种新型流固耦合不可压物质点法,得到了体积加权的压力泊松方程PPE(Pressure Poisson Equation),解决了完全不可压物质点法无法处理不规则边界和移动边界的问题。采用流固耦合不可压物质点法研究了运动刚体容器中的液体晃动问题,并与已有实验和数值结果进行对比,验证了算法的正确性和精度。

As a hybrid meshless method,material point method （MPM） takes advantages of both Eulerian and Lagrangian methods,so it possesses unique advantages in solving fluid-structure interaction （FSI） problems. For free surface flow problems, our group has developed a weakly compressible material point method （WCMPM） and a fully incompressible material point method （iMPM） based on the MPM of MPM. However, both of them suffer from some difficulties in solving FSI problems. The weakly compressible EOS adopted in the WCMPM leads to a very small time step size, serious pressure oscilla- tion and even non-physical spray and splash;The iMPM eliminates the pressure oscillation existing in WCMPM and allows a significantly bigger time step size, but it is difficult to handle the moving solid boundary conditions. In this paper, a novel fIuid-structure interaction incompressible material point method （FSI-iMPM） is proposed based on a variational form projection scheme. A volume-weighted pressure Poisson equation （PPE） is established on the background grid. The proposed FSI-iMPM couples fluid with irregular solid boundary and moving solid wall boundary automatically. To validate the proposed FSI-iMPM, two problems of sloshing in a moving rigid container are investigated, and the numerical results agree well with the available experiment and numerical results.