Well-balanced high-order numerical schemes for one-dimensional blood flow in vessels with varying mechanical properties

Authors:
Lucas O. MüLler;Carlos ParéS;Eleuterio F. Toro
Affiliations:
Laboratory of Applied Mathematics, University of Trento, Trento, Italy;Departamento de Análisis Matemático, Universidad de Málaga, Málaga, Spain;Laboratory of Applied Mathematics, University of Trento, Trento, Italy
Venue:
Journal of Computational Physics
Year:
2013

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Abstract

We construct well-balanced, high-order numerical schemes for one-dimensional blood flow in elastic vessels with varying mechanical properties. We adopt the ADER (Arbitrary high-order DERivatives) finite volume framework, which is based on three building blocks: a first-order monotone numerical flux, a non-linear spatial reconstruction operator and the solution of the Generalised (or high-order) Riemann Problem. Here, we first construct a well-balanced first-order numerical flux following the Generalised Hydrostatic Reconstruction technique. Then, a conventional non-linear spatial reconstruction operator and the local solver for the Generalised Riemann Problem are modified in order to preserve well-balanced properties. A carefully chosen suit of test problems is used to systematically assess the proposed schemes and to demonstrate that well-balanced properties are mandatory for obtaining correct numerical solutions for both steady and time-dependent problems.