一种适用于浸入有限元方法的网格自适应方法

针对动边界流固耦合的数值模拟问题，基于浸入有限元方法提出了一种耦合流场特征和几何特征的笛卡儿网格局部加密自适应方法，克服了单个自适应指示因子无法精确捕捉固体运动的特征的不足。在耦合自适应策略中，分别以流场涡量和固体位置作为流场和几何信息指示因子来驱动网格自适应。通过方腔顶盖驱动圆盘流动算例，以圆盘体积守恒和特征点的运动轨迹验证耦合自适应方法的优势。计算结果表明:仅基于流动特征的自适应不能很好地保证圆盘的体积守恒；仅基于几何特征的自适应无法有效追踪圆盘的轨迹；而耦合自适应策略能同时较好地保证两项指标的计算精度，在保证总体计算自由度不变的情况下，圆盘区域速度散度2-范数降低了一个数量级，圆盘的轨迹误差2-范数降低了2个数量级。 

An adaptive mesh refinement method based on immersed finite element method

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.