Since the 1950s, traffic flows have been the subject of scientific study. Now, 60 years later, they still are. Researchers with backgrounds ranging from engineering over Mathematics and Physics to Chemistry and Thermodynamics have continuously strived for a better description of traffic flow. As the worlds population grows, traffic management is becoming a mounting challenge for many cities and towns across the globe. Increasing attention has been devoted to the modeling, simulation, and visualization of traffic flows to investigate causes of traffic congestion and accidents, to study the effectiveness of roadside hardware, signs and other barriers, to improve policies and guidelines related to traffic regulation, and to assist urban development and the design of highway and road systems. A macroscopic two lane traffic flow model appended with linear density-velocity relationship is considered here. To compute numerical solution of the model as an IBVP, explicit upwind scheme and lax-friedrichs scheme are studied. In order to implement the numerical schemes, numerical simulation is performed for 10 km highway of two lanes.

Muhammad Humayun Kabir has obtained M. Phil. Degree in 2012 from Jahangirnagar University, Dhaka, Bangladesh. Since he then has worked in different research projects in the field of Computational Mathematics: Traffic Flow Simulation. He is the author of several articles in reputed journals and conference proceedings.