Numerical approximation and uncertainty quantification for arterial blood flow models with viscoelasticity

The importance of the study blood flow equations is widely recognized as it a tool to understand circulatory system. Arteries and veins result have both elastic viscous behaviour. Models for first case are much more studied they be simpler still satisfying if compared experimental data. In this paper, we consider model which encompasses viscoelastic response in arterial walls, respectively leading conservative non-conservative We present second-order scheme based on first-order Price-T MUSCL-Hancock strategy. This approach automatically adapts above cases. Then, perform Sensitivity Analysis (SA) Continuous Equation Method (CSEM), whose aim how changes inputs can affect its outputs. particular, sensitivity defined derivative (with respect an uncertain parameter a) solution system taken into consideration. Since CSEM cannot directly applied discontinuous solutions, add source term compensate spikes associated Dirac delta functions that arise variables. One main applications SA uncertainty quantification, investigated Riemann problem well network 37 arteries. Details junctions coupling two or vessels also given.