Numerical Experiments in Complex Haemodynamic Flows. Non-Newtonian Effects

摘要

Numerical experiments for non-trivial flows, close to realistic situations in haemodynamics, are described and interpreted. Two geometries have been selected: an axisymmetric corrugated tube (with periodic boundary conditions) and a 3D bifurcation with an obstructed end (anastomosis). Results concern sensitivity of errors associated to the time-step size and mesh refinement, but essentially consist of the quantitative estimation of non-Newtonian effects based on Casson's rheological model, treated in retarded form. The time-step lag of such effects is the main reason for evaluating the sensitivity of errors. Due to the high computational cost characterizing the problems to be faced, we expect that the present results will be useful when real geometries should be modeled. The main conclusions are that non-Newtonian effects may be relevant (especially for secondary flows) and that, in most cases, for the same level of errors the use of Casson's law does not generate excessive additional computational costs. Thus, within this strategy, the user can accurately solve the problem using this rheological model without having to worry if the non-Newtonian effects are important or not.