An Analysis of a 2x2 Keyfitz-Kranzer Type Balance System with Varying Generalized Chaplygin Gas

TL;DR

This paper analyzes a Keyfitz-Kranzer type system with a varying generalized Chaplygin gas, exploring non-self-similar Riemann solutions and their dependence on time, supported by numerical simulations.

Contribution

It provides a detailed description of non-classical solutions and the impact of time dependence on solution regions in a complex fluid system.

Findings

Identification of non-self-similar Riemann solutions.

Demonstration of time-dependent changes in solution regions.

Numerical confirmation using Lax-Friedrichs scheme.

Abstract

We consider a system of two balance laws of Keyfitz-Kranzer type with varying generalized Chaplygin gas, which exhibits negative pressure and is a product of a function of time and the inverse of a power of the density. The Chaplygin gas is a fluid designed to accommodate measurements for the early universe and late-time universal expansion while obeying the pressure-density-time relation. We produce an explanation and description of the non-self-similar Riemann solutions, including the non-classical singular solutions. We also find that due to a direct dependence on time, a change in the regions allowing for combinations of classical and non-classical singular solutions occurs, therefore a Riemann solution can have different solutions over several time intervals. Our findings are confirmed numerically using the local Lax-Friederichs scheme.