The pressureless transition of Riemann solutions containing composite waves for Aw–Rascle–Zhang model with driver adaptation

In this paper, we focus on the pressureless limiting behaviors of the Riemann solutions for Aw–Rascle–Zhang (ARZ) model with density-adaptive drivers. We construct the Riemann solutions containing composite waves by the “Liu-entropy” condition due to the non-genuine nonlinearity of this traffic flow system. Then we investigate the limiting dynamics of the Riemann solutions and demonstrate the formation of δ−shock waves and vacuum states as the pressure vanishes. Finally, numerical simulations are performed to validate the theoretical results. Two highlights are noteworthy. First, composite waves persist during the pressure vanishing process under certain conditions. Second, we find a new mechanism in cavitation formation that as the pressure vanishes, the Riemann solution containing shock waves converges to the vacuum solution of the pressureless gas dynamics model in specific configurations.