BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Marco F.P. ten Eikelder DTSTART:20260506T070000Z DTEND:20260506T080000Z DTSTAMP:20260512T105021Z UID:MathMAC/61 DESCRIPTION:Title: Thermodynamics and computation of N-phase diffuse-interface flows\nby Marco F.P. ten Eikelder as part of Modelling of materials - theory\, mode l reduction and efficient numerical methods (UNCE MathMAC)\n\n\nAbstract\n Diffuse-interface (phase-field) models provide a versatile framework for i nterfacial dynamics in multiphase fluids. The prototypical diffuse-interfa ce models for incompressible fluid mixtures are the Navier-Stokes Cahn-Hil liard (NSCH) models. Over the last few decades\, many NSCH models with non -matching densities have been proposed. Even though these phase-field mode ls aim to represent the same physical phenomena\, they seem to differ at f irst sight. To explore their connections\, I present unifying frameworks f or both two-phase and N-phase NSCH models with non-matching densities. I t hen show that\, from the perspective of mixture theory\, NSCH models can b e understood as reduced diffuse-interface mixture models in which the evol ution equations for the diffusive fluxes are replaced by constitutive clos ures. This perspective naturally leads to diffuse-interface models that ar e fully compatible with mixture theory and clarifies the relation between classical phase-field formulations and full mixture-theoretic models.\nI w ill then turn to constitutive closure and calibration for N-phase NSCH sys tems. Beyond the standard requirement of reduction consistency when one ph ase is absent\, I consider the stronger condition that physically identica l components can be merged without changing the governing PDEs. This leads to a mixture-aware notion of reduction consistency that strongly constrai ns the admissible constitutive assumptions and\, under a small set of stru ctural axioms\, uniquely determines the free-energy and mobility structure . To enable practical computations\, I will then discuss a thermodynamical ly consistent calibration procedure for N-phase diffuse-interface free ene rgies that determines a symmetric capillarity matrix matching prescribed p airwise surface tensions.\nThe final part of the talk is concerned with co mputation. For incompressible mixtures with two or more constituents\, str ucture-preserving computation is challenging because the numerical method should inherit the rich structure of the continuum model\, including prese rvation of the saturation constraint\, dissipation of the free energy\, an d symmetric treatment of all constituents\, even for arbitrary density rat ios. I will present a symmetric method for incompressible N-phase NSCH mix ture models that retains these properties at the fully discrete level. The talk concludes with representative numerical simulations of N-phase flows .\n LOCATION:https://researchseminars.org/talk/MathMAC/61/ END:VEVENT END:VCALENDAR