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In this work, we present the different steps in the modeling and implementation of a first-order macroscopic road traffic simulation tool, using Lighthill–Whitham–Richards approach with a Godunov scheme (cell transmission model) and bounded acceleration. The origin–destination traffic movement is based on the definition of partial streams according to their chosen paths or 'routes' from an origin to its destination. The resolution of the traffic conflicts at the nodes level is achieved using a modified dynamic node model. The dynamic node model proposed in this work introduces a new supply function which follows from the extension of the Highway Capacity Manual (2010) model for use in dynamic and instantaneous regime. The method is then applied to reconstruct the traffic at a roundabout in the city of Sousse, Tunisia, known to be over-jammed at rush hour. The results are satisfactory and can be generalized to other intersection types with different priority levels. [ABSTRACT FROM AUTHOR]