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Coupling between lumped and distributed models for blood flow problems

By QUARTERONI A., RAGNI S and VENEZIANI A.

Abstract

In this paper we propose a method for coupling distributed\ud and lumped models for the blood circulation. Lumped\ud parameter models, based on an analogy between the circulatory\ud system and an electric or a hydraulic network are\ud widely employed in the literature to investigate different systemic\ud responses in physiologic and pathologic situations. From the mathematical viewpoint\ud these models are represented by ordinary differential\ud equations. On the other hand, for the accurate description\ud of local phenomena, the Navier–Stokes equations for incompressible\ud fluids are considered. In the multiscale perspective,\ud lumped models have been adopted as a numerical\ud preprocessor to provide a quantitative estimate of\ud the boundary conditions at the interfaces. However, the two\ud solvers (i.e. the lumped and the distributed one) have been\ud used separately. In the present work, we introduce a genuinely\ud heterogeneous multiscale approach where the local model\ud and the systemic one are coupled at a mathematical and numerical\ud level and solved together. In this perspective, we have\ud no longer boundary conditions on the artificial sections, but\ud interface conditions matching the two submodels. The mathematical\ud model and its numerical approximation are carefully\ud addressed and several test cases are considered

Year: 2001
OAI identifier: oai:iris.unife.it:11392/2336453
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