36 research outputs found
A tangential regularization method for backflow stabilization in hemodynamics
In computational simulations of fluid flows, instabilities at the Neumann boundaries may appear during backflow regime. It is widely accepted that this is due to the incoming energy at the boundary, coming from the convection term, which cannot be controlled when the velocity field is unknown. We propose a stabilized formulation based on a local regularization of the fluid velocity along the tangential directions on the Neumann boundaries. The stabilization term is proportional to the amount of backflow, and does not require any further assumption on the velocity profile. The perfomance of the method is assessed on a twoand three-dimensional Womersley flows, as well as considering a hemodynamic physiological regime in a patient-specific aortic geometry
A tangential regularization method for backflow stabilization in hemodynamics
In computational simulations of fluid flows, instabilities at the Neumann boundaries may appear during backflow regime. It is widely accepted that this is due to the incoming energy at the boundary, coming from the convection term, which cannot be controlled when the velocity field is unknown. We propose a stabilized formulation based on a local regularization of the fluid velocity along the tangential directions on the Neumann boundaries. The stabilization term is proportional to the amount of backflow, and does not require any further assumption on the velocity profile. The perfomance of the method is assessed on a two- and three-dimensional Womersley flows, as well as considering a hemodynamic physiological regime in a patient-specific aortic geometry
A Stokes-consistent backflow stabilization for physiological flows
In computational fluid dynamics incoming flow at open boundaries, or \emph{backflow}, often yields to unphysical instabilities for
high Reynolds numbers. It is widely accepted that this is due to the incoming energy
arising from the convection term, which cannot be \emph{a priori} controlled when the velocity field is unknown at the boundary.
In order to improve the robustness of the numerical simulations, we propose a stabilized formulation
based on a penalization of the residual of a weak Stokes problem on the open boundary, whose viscous part controls the
incoming convective energy, while the inertial term contributes to the kinetic energy. We also present different strategies
for the approximation of the boundary
pressure gradient, which is needed for defining the stabilization term.
The method has the advantage that it does not require neither artificial modifications or extensions of the
computational domain. Moreover, it is consistent with the Womersley solution. We illustrate our approach
on numerical examples ~- both academic and real-life -~ relevant to blood and respiratory flows. The results also
show that the stabilization parameter can be reduced with the mesh size
Numerical Considerations for Advection-Diffusion Problems in Cardiovascular Hemodynamics
Numerical simulations of cardiovascular mass transport pose significant
challenges due to the wide range of P\'eclet numbers and backflow at Neumann
boundaries. In this paper we present and discuss several numerical tools to
address these challenges in the context of a stabilized finite element
computational framework. To overcome numerical instabilities when backflow
occurs at Neumann boundaries, we propose an approach based on the prescription
of the total flux. In addition, we introduce a "consistent flux" outflow
boundary condition and demonstrate its superior performance over the
traditional zero diffusive flux boundary condition. Lastly, we discuss
discontinuity capturing (DC) stabilization techniques to address the well-known
oscillatory behavior of the solution near the concentration front in
advection-dominated flows.We present numerical examples in both idealized and
patient-specific geometries to demonstrate the efficacy of the proposed
procedures. The three contributions dis-cussed in this paper enable to
successfully address commonly found challenges when simulating mass transport
processes in cardiovascular flows
Modified Navier-Stokes equations for the outflow boundary conditions in hemodynamics
International audienceWe present a new approach for the outflow boundary conditions of Navier-Stokes equations in hemodynamics. We first describe some existing 3D-0D coupling methods and highlight benefits and disadvantages of each of them. We then introduce a new method that consists in adding a 3D artificial part where the Navier-Stokes equations are modified to obtain an equivalent energy balance to a standard coupling with a 3-element Windkessel model. We investigate theoretically the stability of the system and compare it to previously introduced methods. Finally we compare these coupling methods for numerical simulations of blood flow in three patient-specific models, which represent different flow regimes in the pulmonary and systemic circulations. The new method, especially in its hybrid form, is a possible alternative to existing methods. It can be in particular convenient in codes that do not allow users to implement non-standard boundary conditions
Efficient blood flow simulations for the design of stented valve reducer in enlarged ventricular outflow tracts
Tetralogy of Fallot is a congenital heart disease characterized over time, after the initial repair, by the absence of a functioning pulmonary valve, which causes regurgitation, and by progressive enlargement of the right ventricle and pulmonary arteries. Due to this pathological anatomy, available transcatheter valves are usually too small to be deployed in the enlarged right ventricular outflow tracts (RVOT). To avoid surgical valve replacement, an alternative consists in implanting a reducer prior to or in combination with a transcatheter valve. We describe a computational model to study the effect of a stented valve RVOT reducer on the hemodynamics in enlarged ventricular outflow tracts. To this aim, blood flow in the right ventricular outflow tract is modeled via the incompressible Navier--Stokes equations coupled to a simplified valve model, numerically solved with a standard finite element method and with a reduced order model based on Proper Orthogonal Decomposition (POD). Numerical simulations are based on a patient geometry obtained from medical imaging and boundary conditions tuned according to measurements of inlet flow rates and pressures. Different geometrical models of the reducer are built, varying its length and/or diameter, and compared with the initial device-free state. Simulations thus investigate multiple device configurations and describe the effect of geometry on hemodynamics. Forces exerted on the valve and on the reducer are monitored, varying with geometrical parameters. Results support the thesis that the reducer does not introduce significant pressure gradients, as was found in animal experiments. Finally, we demonstrate how computational complexity can be reduced with POD
A mathematical model that integrates cardiac electrophysiology, mechanics, and fluid dynamics: Application to the human left heart
: We propose a mathematical and numerical model for the simulation of the heart function that couples cardiac electrophysiology, active and passive mechanics and hemodynamics, and includes reduced models for cardiac valves and the circulatory system. Our model accounts for the major feedback effects among the different processes that characterize the heart function, including electro-mechanical and mechano-electrical feedback as well as force-strain and force-velocity relationships. Moreover, it provides a three-dimensional representation of both the cardiac muscle and the hemodynamics, coupled in a fluid-structure interaction (FSI) model. By leveraging the multiphysics nature of the problem, we discretize it in time with a segregated electrophysiology-force generation-FSI approach, allowing for efficiency and flexibility in the numerical solution. We employ a monolithic approach for the numerical discretization of the FSI problem. We use finite elements for the spatial discretization of partial differential equations. We carry out a numerical simulation on a realistic human left heart model, obtaining results that are qualitatively and quantitatively in agreement with physiological ranges and medical images