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Reduced one‐dimensional modelling and numerical simulation for mass transport in fluids
Author(s) -
Köppl T.,
Wohlmuth B.,
Helmig R.
Publication year - 2012
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.3728
Subject(s) - discretization , nonlinear system , discontinuous galerkin method , mathematics , galerkin method , dissipation , numerical analysis , mathematical analysis , convection–diffusion equation , robustness (evolution) , finite element method , physics , biochemistry , chemistry , quantum mechanics , gene , thermodynamics
SUMMARY 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.