Numerical Algorithms for Flows in the Nodes of 2D Models of Pipe Networks

Karlin, Vladimir

doi:10.1006/jcph.1996.5609

Cited by 1 publication

(3 citation statements)

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“…The heterogeneous model obtained coupling the Navier-Stokes equations and the ODE system (9) with the interface conditions (11) and (12) is not well posed. Actually, the NavierStokes equations lack the pointwise boundary data required on the those parts of the domain boundaries facing the electrical network.…”

Section: Coupling Of Distributed and Lumped Parameter Modelsmentioning

confidence: 99%

“…Actually, the NavierStokes equations lack the pointwise boundary data required on the those parts of the domain boundaries facing the electrical network. In [8] a method to enforce mean pressure conditions (11) preserving the well posedness of the NavierStokes problem is proposed. It is based on a suitable weak fulfillment of conditions (4), which actually amount to satisfy (11) at least in the case of a straight cylindrical pipe.…”

Section: Coupling Of Distributed and Lumped Parameter Modelsmentioning

confidence: 99%

“…In [8] a method to enforce mean pressure conditions (11) preserving the well posedness of the NavierStokes problem is proposed. It is based on a suitable weak fulfillment of conditions (4), which actually amount to satisfy (11) at least in the case of a straight cylindrical pipe. In the sequel we will always refer to (4) as the mathematically correct interface mean pressure conditions.…”

Section: Coupling Of Distributed and Lumped Parameter Modelsmentioning

confidence: 99%

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Coupling between lumped and distributed models for blood flow problems

Quarteroni

Ragni

Veneziani

2001

Computing and Visualization in Science

127

111

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In this paper we propose a method for coupling distributed and lumped models for the blood circulation. Lumped parameter models, based on an analogy between the circulatory system and an electric or a hydraulic network are widely employed in the literature to investigate different systemic responses in physiologic and pathologic situations (see e.g. [13, 24, 30, 15, 4, 27, 11, 14]). From the mathematical viewpoint these models are represented by ordinary differential equations. On the other hand, for the accurate description of local phenomena, the Navier–Stokes equations for incompressible fluids are considered. In the multiscale perspective, lumped models have been adopted (see e.g. [16]) as a numerical preprocessor to provide a quantitative estimate of the boundary conditions at the interfaces. However, the two solvers (i.e. the lumped and the distributed one) have been used separately. In the present work, we introduce a genuinely heterogeneous multiscale approach where the local model and the systemic one are coupled at a mathematical and numerical level and solved together. In this perspective, we have no longer boundary conditions on the artificial sections, but interface conditions matching the two submodels. The mathematical model and its numerical approximation are carefully addressed and several test cases are considered

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Section: Coupling Of Distributed and Lumped Parameter Modelsmentioning

confidence: 99%