A high-order diffused-interface approach for fully compressible two-phase flow simulations using a Discontinuous Galerkin method

A diffused-interface approach based on Allen-Cahn phase-field equation is developed within a high-order Discontinuous Galerkin framework. The interface capturing technique is based on the balance between an explicit diffusion contribution and a sharpening term in the phase-field equation. The latter term involves the computation of the normal vectors to the interface. Due to the steep profile of the interface, the computation of the normal vectors can be particularly delicate in such conditions. To this end, a non-linear preconditioning strategy is proposed in this work where an additional smooth level-set function is advected by the flow and used for the evaluation of the normal vectors. It is shown that for appropriate choices of numerical fluxes and parameters of the model, the phase-field remains bounded without any need for explicit clipping or mass redistribution. The proposed diffused-interface technique is then implemented within a five equation model for fully compressible two-phase flows. In order to preserve isolated interfaces, a quasi-conservative discretisation of the phase-field equation is employed. A series of numerical experiments are performed to assess the accuracy and robustness of the developed methodology, including inviscid two-phase flows.