Civil Engineering Association

A Computational Framework for Sloshing in Liquid Storage Tank: Theory and Application

On one hand, the mathematical analysis of some free surface flows is considered. A model problem in one space dimension is first investigated. The Burgers equation with diffusion has
to be solved on a space interval with one free extremity. This extremity is unknown and moves in time. The main work is concerned with the simulation of the incompressible
Newtonian fluid flow problem. The space discretisation is based on the stabilized velocitypressure finite element method. The movement and the deformation of the domain are accounted for by employing the arbitrary Lagrangian-Eulerian (ALE) description of the fluid kinematics. The time discretisation is carried out by using implicit, explicit and semi implicit
scheme. The stability and the convergence of time splitting scheme are investigated. A partitioned solution procedure is developed based on the Newton-Raphson methodology
which incorporates full linearization of the overall incremental problem. Accuracy and stability of the solutions are demonstrated in example for which the analytical solutions are known. In the example, the Burger’s equation analogue to 1-D fluid flows is solved without and with FE mesh motion, to show that the mesh motion practically does not affect the solutions. All solutions presented show that the proposed algorithm is sufficiently accurate and stable. Since the algorithm is implicit, high accuracy of results can be achieved with a relatively large time step.A numerical example is provided to demonstrate the efficiency of the methodology by modeling large amplitude sloshing in a rectangular tank.