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将ALE(任意的拉格朗日-欧拉)运动学描述关系引入到Navier-Stokes方程中,在时间域上采用分步离散方法中的速度修正格式,利用Galerkin加权余量方法推导了系统的有限元数值离散方程;推导了考虑表面张力效应时有限元边界条件的弱积分形式。模拟了考虑表面张力情况下圆筒形贮腔中液体的非线性晃动,揭示了考虑表面张力效应时液体非线性晃动的重要特征。
The kinematic description of ALE (arbitrary Lagrange-Euler) is introduced into the Navier-Stokes equations, and the velocity correction format of the stepwise discretization method is used in the time domain. The Galerkin weighted residual method is used to derive the Finite element numerical discretization equation; We derive the weak integral form of the finite element boundary condition considering the surface tension effect. The non-linear sloshing of the liquid in the cylindrical reservoir considering the surface tension is simulated, revealing the important characteristics of the nonlinear sloshing of the liquid in consideration of the surface tension effect.