On the basis of the Navier–Stokes equations in three space dimensions and a convection–diffusion equation, we use a nonlinear system of three hyperbolic PDEs in one space dimension to simulate mass transport. We focus on the modelling of mass transport at a bifurcation of a vessel. For the numerical treatment of the hyperbolic PDE system, we use stabilised discontinuous Galerkin (DG) approximations with a Taylor basis. DG approximations together with a suitable time integration method enable us to simulate wave propagations for many periods avoiding excessive dispersion and dissipation effects. However, standard DG approximations tend to create non-physical oscillations at sharp fronts, and thus stabilisation techniques are required. Finally, we present some numerical results illustrating the robustness of our model and the numerical discretisation.Copyright © 2012 John Wiley & Sons, Ltd.