一种适用于浸入有限元方法的网格自适应方法

For the numerical simulation of fluid-structure interaction with moving boundary, a local Cartesian mesh adaptation method coupling flow field features and geometric features is developed based on immersed finite element method. This method overcomes the inaccuracy of simulating solid motion with a single adaptive indicator. In the coupling adaptation, the vorticity is used as the adaptive indicator factor for flow field, and the solid position is used as the indicator for the geometric feature to drive mesh adaptation. The advantages of the coupling adaptive strategy are verified by a numerical example, disk entrained in a lid-driven cavity flow, with volume conservation of the disk and some points' motion trajectory on disks. The computational results show that the volume conservation of the disk cannot be well guaranteed only by the adaptation based on flow characteristics; the trajectory tracking of the disk cannot be effectively achieved only by the geometry-based adaptation; but the coupling adaptation strategy in this paper can ensure the accuracy of the two indexes at the same time. When the overall computational degrees of freedom remain constant, the 2-norm of divergence of velocity can be reduced by one order of magnitude and the trajectory error 2-norm of the disk is reduced by two orders of magnitude.