Structure of undercompressive shock waves in three-phase flow in porous media

TL;DR

This paper investigates the structure of undercompressive shock waves in three-phase porous media flow, comparing identity and capillarity diffusion matrices, and analyzing their effects on shock solutions and the Riemann problem.

Contribution

It constructs the undercompressive shock surface for different diffusion matrices and analyzes how capillarity influences shock solutions in three-phase flow.

Findings

Similar shock structures for different diffusion matrices

Capillarity matrix affects Riemann problem solutions

Undercompressive shocks satisfy viscous profile criterion

Abstract

Undercompressive shocks are a special type of discontinuities that satisfy the viscous profile criterion rather than the Lax inequalities. These shocks can appear as a solution to systems of two or more conservation laws. This paper presents the construction of the undercompressive shock surface for two types of diffusion matrices. The first type is the identity matrix. The second one is the capillarity matrix associated with the proper modeling of the diffusive effects caused by capillary pressure. We show that the structure of the undercompressive surface for the different diffusion matrices is similar. We also show how the choice of the capillarity matrix influences the solutions to the Riemann problem.