Computational Issues
Flat Surfaces
When a part of the interface is flat, problems could arise. Specifically, a node may move along the interface -- which has no physical significance. To counter this problem, an finite artificial mobility was assigned to each nodal point, altering the weak statement by,
This amounts to adding small number 10-6 to the diagonal positions of the global viscosity matrix.
Boundary Conditions
Boundary conditions were typically setting a particular node to be fixed. The method to do this multiply and add a large number (106) to the nodal's position in the viscosity matrix.
Element Size
During the simulation, elements could become either too large or too small -- effecting the accuracy and computational time. Therefore after each update of nodal positions, the nodal points were ran through a algorithm that eliminated points too close and cut elements in half that were too long.