Riemann solutions and shock wave interactions for a two-velocity isentropic traffic flow

Abstract The study explores the Riemann problem and wave interactions for a two-lane two velocities traffic flow model with ideal isentropic pressure governing 3 × 3 system of hyperbolic conservation laws. Utilizing the method of characteristics, we construct the elementary waves, namely shock waves, rarefaction waves, and contact discontinuities of the Riemann problem in one-parameter family of curves. A condition for the existence of a unique solution is proved on arbitrary initial data which is not necessarily closed. Also, we establish a necessary and sufficient condition to determine whether a shock wave or a rarefaction wave exist of the solution in one-family and three-family of characteristic fields. Further, we analyze the combination of two shocks originating from the same family. Moreover, we solve the Riemann problem in a qualitative manner by considering the projections of the elementary waves in phase plane. At the end, the conditions on initial data are demonstrated to the waves structure of the Riemann problem along with the vacuum state.