A method for simulation of free surface problems is presented.Based on the viscous incompressible Navier-Stokes equations,space discretization of the flow is obtained by the least square finite element method.The time evolution is obtained by the finite difference method.Lagrangian description is used to track the free surface.The results are compared with the experimental dam break results,including water collapse in a 2D rectangular section and in a 3D cylinder section.A good agreement is achieved for the distance of surge front as well as the height of the residual column.
Nonlinear dynamics of liquid-filled rectangular tank with elastic appendages are studied. Based on the assumption of ideal fluid, the coupling dynamic equations of rigid tank, elastic appendages and liquid fuel are derived using H-O principle. In the case of pitch excitation, the modified potential function and wave height function are introduced to describe the moving boundary of fluid, then Galerkin's method is used to discretize the dynamic equations into ordinary differential equations. The natural frequencies of the coupling system are formulated in liquid depth, the length of the tank, etc. The formulae are confirmed by numerical simulations, which also show that the effects of liquid and elastic appendages on the attitude angular of rigid.
