Nonisothermal Richards flow in porous media with cross diffusion

TL;DR

This paper proves the existence of weak entropy solutions for a complex nonisothermal two-phase flow model in porous media, incorporating temperature gradients and cross-diffusion effects, using variational methods and advanced mathematical tools.

Contribution

It introduces a novel existence proof for variational entropy solutions in a thermodynamically consistent nonisothermal flow model with cross diffusion.

Findings

Existence of large-data weak entropy solutions established.

A priori estimates derived from entropy and energy balances.

Use of Div-Curl lemma for compactness in the analysis.

Abstract

The existence of large-data weak entropy 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. Due to the fact that some terms from the total energy balance are non-integrable in the classical weak sense, we consider so-called variational entropy solutions. A priori estimates are derived from the entropy balance and the total energy balance. The compactness is achieved by using the Div-Curl lemma.