A Well-Balanced Discontinuous Galerkin Method for the Blood Flow Model (Journal of Mathematical Study, 2017)
Numerical simulations by high order methods for the blood flow model inarteries have wide applications in medical engineering. This blood flow model admitsthe steady state solutions, for which the flux gradient is non-zero, and is exactly balancedby the source term. In this paper,we design a high order discontinuous Galerkinmethod to this model by means of a novel source term approximation as well as well-balancednumerical fluxes. Rigorous theoretical analysis as well as extensive numericalresults all suggests that the resulting method maintains the well-balanced property,enjoys high order accuracy and keeps good resolutions for smooth and discontinuoussolutions.
Keywords: Blood flow model; discontinuous Galerkin method; well-balanced property; high order accuracy; source term.