Equidistribution algorithm for a two-dimensional phase field model

An iterative equidistribution algorithm is proposed for solving a two-dimensional phase field model, using the finite element method. The phase field equation is used to model a two-phase fluid inside a tube, where the boundary conditions at the walls define the static contact angle. The numerical solution is found by the finite element method with triangular elements, using a structured mesh generated with Delaunay triangulation. First, the adaptive grid algorithm is carefully tested in an analytic function where numerical results demonstrate the accuracy and effectiveness in the adaptive grid generation. Finally, we present numerical results for the phase field model.