arXiv subjects
Publications and source records attributed to Dennis Schumann.
In this work we propose and analyse a structure-preserving approximation of the non-isothermal Cahn-Hilliard-Navier-Stokes system using conforming finite elements in space and implicit time discretisation with convex-concave splitting. The system is first reformulated into a variational form which reveal the structure of the equations, which is then used in the subsequent approximation.
In this research, we introduce and investigate an approximation method that preserves the structural integrity of the non-isothermal Cahn-Hilliard-Navier-Stokes system. Our approach extends a previously proposed technique [1], which utilizes conforming (inf-sup stable) finite elements in space, coupled with implicit time discretization employing convex-concave splitting. Expanding upon this method, we incorporate the unstable P1|P1 pair for the Navier-Stokes contributions, integrating Brezzi-Pitkäranta stabilization. Additionally, we improve the enforcement of incompressibility conditions through grad div stabilization. While these techniques are well-established for Navier-Stokes equations, it becomes apparent that for non-isothermal models, they introduce additional coupling terms to the equation governing internal energy. To ensure the conservation of total energy and maintain entropy production, these stabilization terms are appropriately integrated into the internal energy equation.