A Discontinuous Galerkin Method for Blood Flow and Solute Transport in One-Dimensional Vessel Networks

This paper formulates an efficient numerical method for solving the convection diffusion solute transport equations coupled to blood flow equations in vessel networks. The reduced coupled model describes the variations of vessel cross-sectional area, radially averaged blood momentum and solute concentration in large vessel networks. For the discretization of the reduced transport equation, we combine an interior penalty discontinuous Galerkin method in space with a novel locally implicit time stepping scheme. The stability and the convergence are proved. Numerical results show the impact of the choice for the steady-state axial velocity profile on the numerical solutions in a fifty-five vessel network with physiological boundary data.