A high‐order local time stepping finite volume solver for one‐dimensional blood flow simulations: application to the ADAN model. (26th January 2016) - Müller, Lucas O.; Blanco, Pablo J.; Watanabe, Sansuke M.; Feijóo, Raúl A.
Summary: In recent years, the complexity of vessel networks for one‐dimensional blood flow models has significantly increased, because of enhanced anatomical detail or automatic peripheral vasculature generation, for example. This fact, along with the application of these models in uncertainty quantification and parameter estimation poses the need for extremely efficient numerical solvers. The aim of this work is to present a finite volume solver for one‐dimensional blood flow simulations in networks of elastic and viscoelastic vessels, featuring high‐order space‐time accuracy and local time stepping (LTS). The solver is built on (i) a high‐order finite volume type numerical scheme, (ii) a high‐order treatment of the numerical solution at internal vertexes of the network, often called junctions, and (iii) an accurate LTS strategy. The accuracy of the proposed methodology is verified by empirical convergence tests. Then, the resulting LTS scheme is applied to arterial networks of increasing complexity and spatial scale heterogeneity, with a number of one‐dimensional segments ranging from a few tens up to several thousands and vessel lengths ranging from less than a millimeter up to tens of centimeters, in order to evaluate its computational cost efficiency. The proposed methodology can be extended to any other hyperbolic system for which network applications are relevant. Copyright © 2016 John Wiley & Sons, Ltd. Abstract : The increasing complexity of vessel networks for 1D blood flow models, motivated by anatomical detail or automatic network generation, for example, poses the need for extremely efficient numerical solvers. As a possible answer to this requirement, we present a high‐order, finite volume‐type algorithm featuring local time stepping (LTS). The scheme is applied to simple and anatomically detailed one‐dimensional arterial networks. Simulation time speed‐ups of the LTS scheme with respect to the conventionally used global time‐stepping strategy are extremely significant.