Page 401 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 401
MULTICOMPONENT DIFFUSION IN POROUS MEDIA (MS-42)
solid governed by a hyperbolic evolution and an incompressible fluid governed by the (n-
dimensional) Navier-Stokes equations for n ≥ 2.
Nonisothermal Richards flow in porous media with cross diffusion
Nicola Zamponi, zamponi@karlin.mff.cuni.cz
University of Mannheim, Germany
Coauthors: Esther Daus, Pina Milišic´
The existence of large-data weak solutions to a nonisothermal immiscible compressible two-
phase unsaturated flow model in porous media is proved. The model is thermodynamically
consistent and includes temperature gradients and cross-diffusion effects. So-called variational
entropy solutions, which involve the integrated total energy balance, are considered in order to
overcome the lack of integrability of some terms in the total energy flux. A priori estimates are
derived from the entropy balance and the total energy balance. A sequence of approximated
solutions is built via a time semi-discretization and several regularizations. The compactness of
the sequence of approximated solutions is achieved by using the Div-Curl lemma.
The Boltzmann gas equation in relation to Onsager–Stefan–Maxwell
diffusion for Lennard-Jones gas mixtures
Maxim Zyskin, maxim.zyskin@eng.ox.ac.uk
University of Oxford, United Kingdom
Coauthor: Charles W. Monroe
The Enskog method is an asymptotic method that provides solutions of the Boltzmann equa-
tion close to local equilibrium. The method predicts kinetic properties of gases, such as Ste-
fan–Maxwell diffusivities, in terms of certain collision integrals. We describe a method to com-
pute collision integrals, and a method of molecular dynamics simulation of Stefan–Maxwell
diffusivities based on Onsager’s regression hypothesis. We investigate how analytical pre-
dictions compare with molecular dynamics simulations for mixtures of Lennard-Jones gases
and experiments with mixtures of monatomic gases. We apply the Enskog method to derive
continuum-level model equations. Within the limitations of Enskog’s method, these results
identify with a set of multi-species transport equations that Goyal and Monroe recently derived
using the alternative theory of irreversible thermodynamics.
399
solid governed by a hyperbolic evolution and an incompressible fluid governed by the (n-
dimensional) Navier-Stokes equations for n ≥ 2.
Nonisothermal Richards flow in porous media with cross diffusion
Nicola Zamponi, zamponi@karlin.mff.cuni.cz
University of Mannheim, Germany
Coauthors: Esther Daus, Pina Milišic´
The existence of large-data weak solutions to a nonisothermal immiscible compressible two-
phase unsaturated flow model in porous media is proved. The model is thermodynamically
consistent and includes temperature gradients and cross-diffusion effects. So-called variational
entropy solutions, which involve the integrated total energy balance, are considered in order to
overcome the lack of integrability of some terms in the total energy flux. A priori estimates are
derived from the entropy balance and the total energy balance. A sequence of approximated
solutions is built via a time semi-discretization and several regularizations. The compactness of
the sequence of approximated solutions is achieved by using the Div-Curl lemma.
The Boltzmann gas equation in relation to Onsager–Stefan–Maxwell
diffusion for Lennard-Jones gas mixtures
Maxim Zyskin, maxim.zyskin@eng.ox.ac.uk
University of Oxford, United Kingdom
Coauthor: Charles W. Monroe
The Enskog method is an asymptotic method that provides solutions of the Boltzmann equa-
tion close to local equilibrium. The method predicts kinetic properties of gases, such as Ste-
fan–Maxwell diffusivities, in terms of certain collision integrals. We describe a method to com-
pute collision integrals, and a method of molecular dynamics simulation of Stefan–Maxwell
diffusivities based on Onsager’s regression hypothesis. We investigate how analytical pre-
dictions compare with molecular dynamics simulations for mixtures of Lennard-Jones gases
and experiments with mixtures of monatomic gases. We apply the Enskog method to derive
continuum-level model equations. Within the limitations of Enskog’s method, these results
identify with a set of multi-species transport equations that Goyal and Monroe recently derived
using the alternative theory of irreversible thermodynamics.
399
