Impact of dissipation ratio on vanishing viscosity solutions of the Riemann problem for chemical flooding model

TL;DR

This paper investigates how the dissipation ratio influences vanishing viscosity solutions in the Riemann problem for chemical flooding models, revealing the emergence of non-classical shocks and their dependence on dissipation parameters.

Contribution

It provides a classification of phase portraits and analyzes shock velocity dependence, advancing understanding of non-monotonic flow effects in chemical flooding models.

Findings

Non-classical undercompressive shocks appear with non-monotonic flow functions.

Shock velocity depends monotonically on the dissipation ratio.

Phase portrait classification aids in understanding shock structures.

Abstract

The solutions for a Riemann problem arising in chemical flooding models are studied using vanishing viscosity as an admissibility criterion. We show that when the flow function depends non-monotonically on the concentration of chemicals, non-classical undercompressive shocks appear. The monotonic dependence of the shock velocity on the ratio of dissipative coefficients is proven. For that purpose we provide the classification of the phase portraits for the travelling wave dynamical systems and analyze the saddle-saddle connections.