Computation of the free surface of a liquid with surface tension for any tank geometry

摘要

To study the dynamics of a tank (container) partially filled of a liquid, in low-gravity or microgravity environment, we first have to find the static position of this system. In this paper, we present a 3D finite element resolution to find this equilibrium configuration for any tank geometry. Both gravity and capillary effects (surface tension) are taken into account. The nonlinear equations of the problem are derived from the differentiation of the total potential energy of the system, then the problem is transformed to the liquid free surface form finding. The well-known singularity of such a problem is regularized using the Updated Reference Strategy. The problem is finally solved using the Newton-Raphson algorithm, with a standard finite element discretization. No restriction on the finite element type is necessary. The tank geometry is given by a finite element model so we can easily treat very complex cases. Several examples illustrate the effectiveness of this method.