Riemann Problem for a Two‐Lane Traffic Model in Dusty Gas Flow

ABSTRACT In this work, we deal with the Riemann solution for a 3 by 3 macroscopic two‐lane traffic flow model of two distinct velocities and equal vehicle density in each lane, along with dust particles obeying the Mie–Grüneisen type equation of state. Based on the characteristic field analysis, we discuss the properties of rarefaction waves, shocks, and contact discontinuities elaborately. For every combination of elementary waves, we provide a solution strategy and derive the two nonlinear algebraic equations of two unknowns. Further, the existence‐uniqueness of the Riemann solution is established locally for arbitrary initial data. Moreover, we apply the Newton–Raphson method for the nonlinear algebraic equations to obtain densities across the middle characteristic field. In the end, we have elaborately discussed the influence of the mass fraction and volume fraction of solid particles in physical quantities with a series of test cases.