A network method for homogeneous, thermally expandable two-phase flow on unstructured triangular grids

Abstract Recently, a numerical method was proposed for the solution of the equations of an incompressible fluid on a two dimensional grid consisting of Delaunay triangles. The method utilized the complementary grid of Voronoi polygons, as well as the dual variable reduction scheme developed by the authors. In this paper we generalize these ideas to thermally expandable, homogeneous, two-phase flow. This includes a derivation of the semi-discrete system, and the dual variable methodology that is used to solve it.