A discontinuous Galerkin finite element method for multiphase viscous flow

Multiphase viscous flow is usually modelled by a coupled system of differential equations comprising hyperbolic partial differential equations describing the evolution of the volume fraction of each phase, and elliptic partial differential equations describing quasi–static force balances. A discontinuous Galerkin finite element method is derived for this system of equations by appealing to conservation of flux and stress of each phase across element boundaries. One and two dimensional examples are used to demonstrate: (i) the long time stability of this method for problems where sharp gradients in solution variables develop as time evolves; and (ii) the superiority of this technique over the continuous Galerkin finite element method for these exemplar problems