We design consistent discontinuous Galerkin finite element schemes for the approximation of a quasi-incompressible two phase flow model of Allen-Cahn/Cahn-Hilliard/Navier-Stokes-Korteweg type which allows for phase transitions. We show that the scheme is mass conservative and monotonically energy dissipative. In this case the dissipation is isolated to discrete equivalents of those effects already causing dissipation on the continuous level, that is, there is no artificial numerical dissipation added into the scheme. In this sense the methods are consistent with the energy dissipation of the continuous PDE system.
|Number of pages||27|
|Journal||ESAIM: Mathematical Modelling and Numerical Analysis|
|Early online date||30 Jan 2015|
|Publication status||Published - 31 Jan 2015|
- 65M12, 65M60, 76T99, 76D45