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Faculty of Science

Department of Mathematics & Statistics













Applied Math Seminar | Ionut Danaila (University of Rouen Normandy)
	
 Jul 3, 2025 
 10:30AM to 11:30AM




































Date/Time

Date(s) - 03/07/2025
10:30 am - 11:30 am





Speaker: Ionut Danaila (University of Rouen Normandy)


Location: Hamilton Hall, Room 207


Title: Coupling Navier-Stokes equations with other PDEs: applications to phase-change materials and two-fluid quantum flows


Abstract: In the first part of the talk I will present the coupling of Navier-Stokes equations with an enthalpy equation modeling a liquid-solid phase change system. The resulting model is used to simulate the coupling between thermal convection and melting/solidification, which is a key phenomenon in many applications, ranging from geophysical flows (Earth’s mantle formation,  magma oceans) to the energy storage or passive temperature control devices using phase-change materials (PCMs). The numerical method uses a new single domain numerical approach to solve the 2D/3D Navier-Stokes-Boussinesq equations for phase-change systems with natural convection.  Numerical simulations of different PCM configurations (PCM with both lateral and basal heating, tubes or layers of PCM) will be presented.




The second part of the talk will be devoted to a new numerical model to couple a Navier-Stokes incompressible fluid with a Gross-Pitaevskii superfluid. The model is used to describe liquid helium II, in which  a normal fluid and a superfluid coexist with independent velocity fields at intermediate temperatures between zero and 2.17 K. The new numerical system is validated against well-known benchmarks for the evolution in a normal fluid of different types or arrangements of quantized vortices (vortex crystal, vortex dipole and vortex rings).