The article introduces a kinetic scheme to solve the 1D Euler equations of hemo-dynamics, and presents comparisons of a closed-loop 1D-0D model with real measurements obtained after the hepatectomy of four pigs. Several benchmark tests show that the kinetic scheme compares well with more standard schemes used in the literature, for both arterial and venous wall laws. In particular, it is shown that it has a good behavior when the section area of a vessel is close to zero, which is an important property for collapsible or clamped vessels. The application to liver surgery shows that a model of the global circulation, including 0D and 1D equations, is able to reproduce the change of waveforms observed after different levels of hepatectomy. This may contribute to a better understanding of the change of liver architecture induced by hepatectomy.