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Conference Papers Year : 2013

A new approach for the outflow boundary condition in three-dimensional hemodynamics


The three-dimensional Navier-Stokes simulation of blood flow and pressure in large vessels requires inlet or outlet boundary conditions that incorporate reduced models of the rest of the circulation (typically 1D or 0D models). Reverse flow may occur in part of or on entire coupling boundaries due to physiological conditions or complex geometry. This warrants careful coupling conditions, so that the scheme is stable, without artificially altering the local flow dynamics. The first idea that comes in mind consists in enforcing the pressure at this coupling boundary to be uniform, that is, the pressure coming from the reduced model. However, such a condition does not appear as the standard boundary condition in most formulations. In fact, in the latter, the traction appears as the natural boundary condition and its normal component is thus enforced to be the uniform reduced model pressure. This energetically generates a convective boundary term that can be destabilizing in the presence of reverse flow. Actually, other Navier-Stokes formulations rather involve the total pressure, which has been shown to lead to an energetically stable coupling between 3D and reduced models of blood flow. Some of these authors have been expecting instabilities when the dynamic pressure is not included in the boundary condition but did not see them numerically. In our experience and the experience of others, numerical instabilities do actually arise, in the presence of reverse flow. A dissipative stabilization has been proposed to counteract the destabilizing effect of the convective boundary term in such a case. In all these methods, the reduced model pressure is imposed as a uniform boundary condition for the Navier-Stokes equations. But in complex flow, such as with reverse flow, there is a priori no reason that the normal traction or the total pressure are uniform on a coupling boundary. In this work, we propose to handle the outflow boundary conditions by coupling the 3D Navier-Stokes equations with another 3D compartment. This artificial compartment involves modified Navier-Stokes equations that mimick a three-element Windkessel model (as an example of reduced model). The advantages of such approach are that the coupling 1) does not enforce the traction at the interface to be uniform, and 2) is energetically close to the usual 3D Navier-Stokes - Windkessel one, without the potentially destabilizing convective boundary term. Numerical tests will be presented to compare these methods in patient- specific geometries of various pathophysiological complexities.
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hal-00918648 , version 1 (13-12-2013)


  • HAL Id : hal-00918648 , version 1


Grégory Arbia, Irene Vignon-Clementel, T.-Y. Hsia, Jean-Frédéric Gerbeau. A new approach for the outflow boundary condition in three-dimensional hemodynamics. MPF 2013 - V International Symposium on Modelling of Physiological Flows, CMCS - Ecole Polythecnique Fédérale de Lausanne and MOX - Politecnico di Milano, Jun 2013, Chia, Italy. ⟨hal-00918648⟩
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