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A new two-dimensional model for blood flows in arteries with arbitrary crosssections is derived. The model consists of a system of balance laws forconservation of mass and balance of momentum in the axial and angulardirections. The equations are derived by applying asymptotic analysis to theincompressible Navier-Stokes equations in narrow, large vessels and integratingin the radial direction in each cross section. The main properties of thesystem are discussed and a positivity-preserving well-balanced central-upwindscheme is presented. The merits of the scheme will be tested in a variety ofscenarios. In particular, numerical results of simulations using an idealizedaorta model are shown. We analyze the time evolution of the blood flow underdifferent initial conditions such as perturbations to steady states consistingof a bulging in the vessel's wall. We consider different situations given bydistinct variations in the vessel's elasticity.

A new two-dimensional blood flow model with arbitrary cross sections