The rapid development of social economy speeds up urbanization, but also brings urban traffic congestion and urban traffic problems, such as frequent accidents, energy consumption and environmental pollution. Road traffic, as a part of the most important components in city traffic, is a complex system problem. To solve the difficulties in current city development and people's production and living, and to promote the development of national economy and society greatly, we need to study the road traffic. In order to solve the problem of complex road traffic system influenced by many factors, a physics model of pseudo-fluid of macroscopic road traffic system is established in combination with the traditional Lighthill-Whitham-Richards physics model based on kinetic theory of granular flow. A coupling method of meshless particles with grid is adopted to solve the new traffic model, which is then applied to solving the typical traffic problems. In the new model, vehicles are likened to hard particles. Car-following is likened to collision interactions between particles. Driver driving affected by known road conditions is likened to the driving force exerted by external fluid in two-phase system consisting of fluid and particle, and the influence of vehicles in different lanes is likened to viscous effect between particles. Thus the pseudo-fluid model of road traffic system is deduced and established based on the kinetic theory of granular flow. Then, the traffic multiphase system model is established by adding pedestrians and other non-motorized vehicles to the particles with different attributes. The boundary model of road traffic system based on pipeline theory is established through comparing the boundary model of traffic lights, barricades and forbidden lane changes to wall boundary conditions. Therefore, a complex large traffic model with different initial and boundary conditions considering the complex factors of the system is established. The Smoothed discrete particle hydrodynamics (SDPH) is used to discretize the vehicle system model. A one-to-one correspondence between SDPH vehicles and real vehicles is established through adding the vehicle flow properties characterized by SDPH particles. Then the two-fluid model of road traffic system is solved by combining the finite volume method. Thus, a new simulation approach to solving the macroscopic model of traffic flow is established. Finally, the effects of mixed flow composed of motorized and non-motorized vehicles and vehicles merging on the road traffic are simulated by employing the established model and method. The real-time distribution of the vehicle on the road is obtained, and the variation of the vehicle flow density with time is analyzed. The simulation results are in good agreement with the measured values, which shows that the new model and method are effective and reliable, and they provide a new way of solving the road traffic problem.