Solving Contact Problems With Free Surfaces Using A Lagrangian Meshless Scheme.

Abstract

A combination between a meshless method and a Lagrangian formulation will be
presented. The capability of the meshless methods for solving complicated geometries and the
natural way that Lagrangian formulations have to represent problems with big deformations
of the domain will be put together in this work. The resulting approach showed to be robust
from the CFD point of view and easy to implement from the computational point of view. All
contacts and free surface calculations are embedded in the meshless method, making their
computation straight forward. Lagrangian formulations also have the advantage of solving
the convection of velocity by moving the material points, thus avoiding the tedious convection
terms in the Navier-Stokes equations. As a meshless method, the Meshless Finite Element
Method has been implemented. This method conserves the useful properties of the Finite
Element Method so adding the benefits of the meshless methods. The connection between
material points is calculated using the Extended Delaunay Tessellation. To solve Finite
Element, simplicial elements are used in most of the domain, except when the element quality
is not good enough, then polyhedrons are taken automatically as elements. The Non-
Sibsonian shape function adapts to the polyhedrons keeping the good properties that Finite
Element shape functions have. The presented scheme has found to have remarkable results in
a large variety of contact problems with free surfaces.