Contributed Talk
Consistent treatment of boundary conditions for viscoelastic arterial networks governed by conservative laws with relaxation terms
University of Ferrara, Italy
Abstract
A noteworthy aspect of computational haemodynamics is the modelling of the mechanical interaction between blood and vessel walls. The complete viscoelastic characterisation of this latter leads to numerical results close to physiological evidence. In this work, viscoelasticity is considered in arterial networks via the Standard Linear Solid Model, allowing the introduction of a viscoelastic constitutive tube law in the governing system of equations. The implementation of the viscoelastic contribution at boundaries (inlet, outlet and internal junctions), is performed relying on the hyperbolic nature of the mathematical model. A non-linear system is formulated based on the definition of the Riemann Problem at junctions, characterised by rarefaction waves separated by contact discontinuities, among which the mass and the total energy are conserved. The numerical model consists of an asymptotic-preserving IMEX-SSP(3,3,2) Runge-Kutta Finite Volume scheme. An L-stable diagonally implicit Runge-Kutta (DIRK) scheme is chosen to treat the stiff source terms in the governing system, given by the viscoelasticity, to ensure elevated robustness. The chosen numerical model is proven to be second-order accurate in the whole domain and well-balanced, even when including junctions. Two different benchmark models of the arterial network are implemented, differing in geometry and viscoelastic parameters. The hysteresis loops in the arterial sites of the two networks highlight the high sensitivity of the model to the chosen viscoelastic parameters.