Finite volume and WENO scheme in one-dimensional vascular system modelling

A finite volume and WENO model is developed, validated and applied to a one-dimensional numerical investigation of the vascular system. Suitable balance laws are spatially integrated using a finite volume WENO approach. Time integration is performed using a five steps, fourth order accurate Runge–Kutta strong stability preserving scheme. A detailed investigation of different sets of reflecting and non-reflecting boundary conditions is performed to achieve a correct representation of limited portions of the vascular system. Moreover, special attention is devoted to the numerical discretisation of the source term. Finally, as an application of the whole model, the effect of an abdominal aorta aneurysm on the blood flow is evaluated.