Abstract
The TV-HLL solver for the numerical solution of fluid flow inside elastic vessels is constructed in this paper. The system of partial differential equations describing the fluid flow inside collapsible tubes is presented and solved numerically by using the finite volume method. The evaluation of the numerical flux at the interfaces is performed by using the TV-HLL scheme which is derived from the previous studies presented for solving the Euler equations (Tiam and Tchuen, 2014, 2015). Indeed, the present scheme is obtained by following the Toro-Vazquez splitting, and using the HLL algorithm with modified wave speeds for the pressure system. An essential feature of the TV-HLL scheme is to associate two systems of differential equations, called the advection system and the pressure system. The proposed scheme preserves the non-negativity of essentially nonnegative quantities (cross section). It has been applied to some one-dimensional numerical tests dealing with the fluid flow through the male urethra and the blood flow inside cerebral vessels.
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