| Abstract: |
| In this talk, we present a conforming finite element method for the quasi-incompressible Navier--Stokes--Maxwell--Stefan system.
The model couples the Navier--Stokes equations with a quasi-incompressibility constraint and a cross-diffusion Maxwell--Stefan system describing multicomponent mass transport.
\noindent Our scheme combines a mixed explicit--implicit time discretization with a spatially conforming finite element approximation, ensuring the preservation of partial masses, strict enforcement of the quasi-incompressibility condition, and dissipation of a discrete analogue of the total energy.
Furthermore, we present an a priori error analysis of the fully discrete scheme based on the relative entropy method.
The proof leverages the structure-preserving properties of the discretization, including discrete energy dissipation and the control of the cross-diffusion terms.
Numerical experiments in two space dimensions complement the analysis. They illustrate the predicted convergence rates, confirm the robustness of the error estimate, and demonstrate the correct qualitative behaviour of multicomponent flows, including mass conservation and energy decay.
The results show that the proposed scheme provides a reliable and physically consistent computational framework for the simulation of quasi-incompressible multicomponent fluid mixtures. If time permits we will discuss extensions to the non-isothermal case.
This is joint work with Ansgar J\ungel and Maria Lukacova-Medvidova |
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