Interactions Of Waves For The Aw-Rascle Traffic Flow Model With Modified Chaplygin Gas Pressure

The modified Chaplygin gas is a supplement and extension of Chaplygin gas and generalized Chaplygin gas. It can be used to preferably characterize the phenomenon of the current accelerated boom and inflation of the universe. This thesis studies the interactions of classical waves for Aw-Rascle traffic flow model with modified Chaplygin gas pressure.Firstly, the Riemann problem of Aw-Rascle traffic flow model with modified Chaply-gin gas state equation is solved. By using the phase plane analysis method, the Riemann solutions involving rarefaction waves, shock waves and contact discontinuities are ob-tained constructively. Then, we study the interactions of classical waves. By virtue of the characteristic plane analysis method, six different configurations of Riemann solutions are established. Furthermore, using the second-order nonoscillatory central scheme, we confirm the theoretical analysis numerically.