A predictive continuum dynamic user-optimal model is extended to investigate the traffic equilibrium problem for a polycentric urban city with multiple central business districts (CBDs). The road network within the city is assumed to be dense and can be viewed as a continuum in which travellers can choose their routes in a two-dimensional space. Travellers are assumed to choose their route to minimise the actual total cost to the destination (i.e. the CBD). The model consists of two parts: the conservation law part and the Hamilton–Jacobi part. The finite volume method is used to solve each part on unstructured meshes. Because the two parts are closely interconnected and have different initial times, solving the model can be treated as a fixed-point problem, which is solved using a self-adaptive method of successive averages. Numerical experiments for an urban city with two CBDs are presented to demonstrate the effectiveness of the model and the numerical algorithm.
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