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In this paper, we propose a direct Eulerian generalized Riemann problem (GRP)scheme for a blood flow model in arteries. It is an extension of the EulerianGRP scheme, which is developed by Ben-Artzi, et. al. in J. Comput. Phys.,218(2006). By using the Riemann invariants, we diagonalize the blood flowsystem into a weakly coupled system, which is used to resolve rarefaction wave.We also use Rankine-Hugoniot condition to resolve the local GRP formulation. Wepay special attention to the acoustic case as well as the sonic case. Theextension to the two dimensional case is carefully obtained by using thedimensional splitting technique. We test that the derived GRP scheme is secondorder accuracy.

A direct Eulerian GRP scheme for a blood flow model in arteries