Riemann solutions of the anti-Chaplygin pressure Aw–Rascle model with friction

2022/12/01 by Shiwei Li
Mathematics · Engineering · #Geometric Analysis and Curvature Flows #Fluid Dynamics and Turbulent Flows

paper · doi:10.1063/5.0092054

Abstract

The Riemann problem for the anti-Chaplygin pressure Aw–Rascle model with a Coulomb-like friction term is considered. With the use of the substitution of variables, the Riemann solutions with two or three kinds of different structures involving the delta shock wave in two cases are constructed. The delta shock wave may be used to explain the serious traffic jam. The position, strength, and propagation speed of the delta shock wave are obtained by solving the generalized Rankine–Hugoniot relation under an entropy condition. Moreover, the results show that all waves including the contact discontinuity, rarefaction wave, shock wave, and delta shock wave are bent into parabolic shapes and the Riemann solutions are no longer self-similar under the influence of the Coulomb-like friction term.

Citations

• Approaching Chaplygin pressure limit of solutions to the Aw–Rascle model
• Delta-Shock Waves as Limits of Vanishing Viscosity for Hyperbolic Systems of Conservation Laws
• Formation of delta shocks and vacuum states in the vanishing pressure limit of Riemann solutions to the perturbed Aw–Rascle model
• Exact Riemann solutions for the drift-flux equations of two-phase flow under gravity

Related

• The Riemann solution to the Chaplygin pressure Aw-Rascle model with Coulomb-like friction and its vanishing pressure limit
• Intrinsic phenomena of delta shock waves in a more realistic Chaplygin Aw-Rascle model
• Vanishing Pressure Limit of Solutions to the Aw-Rascle Model for Modified Chaplygin gas
• Limits of solutions to the Aw-Rascle traffic flow model with generalized Chaplygin gas by flux approximation
• The Vanishing Pressure Limits of Riemann Solutions to the Chaplygin Euler Equations