Papaioannou J.G., Dimakopoulos Y., Tsamopoulos J.A.
Because of the three dimensional nature of many physical problems encountered in industrial processes and applications, we develop a novel 3D elliptic grid generator for the construction and the deformation of structured grids. The specific application we consider is related to the large deformations of an air bubble in a liquid between two parallel plates. The new technique is based on the inverted Laplace equations along with internal constraints, which are considered essential in order to adjust grid spacing. This set of equations is accompanied with appropriate set of boundary conditions that is the imposition of the 1D differential arc-length at each of the two coordinates of the boundary surfaces in the computational domain. The new 3D grid generator provides the smoothness of the coordinate lines not only in the bulk, but also on the boundary surfaces. The kinematic condition is invoked for the motion of the 3D surface of the bubble and we also consider the free motion of the 2D contact line (points where the air in the bubble and the surrounding liquid meet the solid boundary). In order to resolve better the flow field and the shape of the bubble free surface we have also developed a local mesh refinement technique. In this way the demand for computational memory is overly reduced. Our method in 3D grid generation follows the Arbitrary Lagrangian Eulerian (A.L.E.) formulation, which when combined with the finite element/Galerkin method provides a flexible and robust tool for simulating free surface flows in three dimensions.
3D simulations, Continuum mechanics, Elliptic mesh generator, Free surface flows