Augmented Riemann solver for urethra flow modeling

In this paper we propose a new conservative numerical scheme for the male urethra and ureter fluid flow simulations. We use finite volume method based on technique of augmented system. Main goal is to construct such conservative scheme which maintains not only some special steady states but all possible ones. Furthermore this scheme should preserve non-negativity of essentially nonnegative quantities from their physical fundamental (here it is the cross-section of the urethra and ureter). Our scheme can be also modified to the high order scheme. At the end we present some numerical experiments.