Stabilised dG-FEM for incompressible natural convection flows with boundary and moving interior layers on non-adapted meshes

摘要

This paper presents heavily grad-div and pressure jump stabilised, equal- andmixed-order discontinuous Galerkin finite element methods for non-isothermalincompressible flows based on the Oberbeck-Boussinesq approximation. In thisframework, the enthalpy-porosity model for multiphase flow in melting andsolidification problems can be employed. By considering the differentiallyheated cavity and the melting of pure gallium in a rectangular enclosure, it isshown that both boundary layers and sharp moving interior layers can be handlednaturally by the proposed class of non-conforming methods. Due to thestabilising effect of the grad-div term and the robustness of discontinuousGalerkin methods, it is possible to solve the underlying problems accurately oncoarse, non-adapted meshes. The interaction of heavy grad-div stabilisation anddiscontinuous Galerkin methods significantly improves the mass conservationproperties and the overall accuracy of the numerical scheme which is observedfor the first time. Hence, it is inferred that stabilised discontinuousGalerkin methods are highly robust as well as computationally efficientnumerical methods to deal with natural convection problems arising inincompressible computational thermo-fluid dynamics.