Reduced one‐dimensional modelling and numerical simulation for mass transport in fluids

Abstract

SUMMARYOn 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.