Abstract:
Traffic flow in most urban areas is augmenting due to the growth in transport and continual demand for it. It is multimodal
and includes use of different types vehicles, motorcycles andeven walking. The assessment of uninterrupted traffic flow is
traditionally based on empirical methods. This study was based on the macroscopic model which is a mathematical model
that formulates the relationships among traffic flow characteristics like density, flow, mean and speed of a traffic stream.
The study considered traffic models first developed by Lighthill and whitham(1955) and later Richards (1956) shortly
Called LW R traffic flow model. Simulation by use of this method enables control strategies of congestion dissipation
and has suggested some recommended measures to rationalize the design of roads and implementation of regulations of
road users considering some regulations and infrastructural gaps in Kisi town. This paper focus on two finite difference
schemes, that is, first order Explicit Upwind Difference Scheme-EUDS (forward time. backward space) and Second order
Lax-Wendroff Difference Scheme-LW DS (forward time centred space) for solving first order PDE as well the traffic
density ρ(t, x) was computed by solving LW R macroscopic conservation form of traffic flow model using both schemes.
The conditions of stability were numerically verified and it is shown that LW DS is superior to EUDS in terms of time step
selection. The results obtained were becompared with average key data which provide initial conditions and boundary data
used for numerical simulation
