带自由面流体运动的拉格朗日有限元分析

Free surface fluid flow analysis by Lagrangian finite element method

介绍了拉格朗日描述下的非定常不可压缩带自由面流体运动的有限元分析。在时间积分中采用速度修正法,采用速度修正分步法不仅可以让速度和压力均采用同阶插值函数,而且可以使算法变得更简单。用四边形单元对所求区域加以划分,并借助于Galerkin加权余量法导出相应的有限元方程组。通过实例计算,阐明了用该方法来分析带自由面流体运动的有效性及其实用性。

A finite element analysis is presented based on the Lagrangian description for unsteady incompressible fluid flow problems with a free surface. For the integration in time, the velocity correction method is used.The same order interpolation functions for velocity and pressure can be employed in the velocity correction fractional step method. The fluid domain is divided by quadrilateral elements. And the finite element equations are derived by Galerkin method.Finally,two numerical examples are provided to confirm the effectiveness of the method.