166 research outputs found
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
A validated patient-specific FSI model for vascular access in haemodialysis
The flow rate inside arteriovenous fistulas is many times higher than physiological flow and is accompanied by high wall shear stress resulting in low patency rates. A fluid–structure interaction finite element model is developed to analyse the blood flow and vessel mechanics to elucidate the mechanisms that can lead to failure. The simulations are validated against flow measurements obtained from magnetic resonance imaging data
Efficient and Higher-Order Accurate Split-Step Methods for Generalised Newtonian Fluid Flow
[EN] In numerous engineering applications, such as polymer or blood flow, the dependence
of fluid viscosity on the local shear rate plays an important role. Standard techniques using
inf-sup stable finite elements lead to saddle-point systems posing a challenge even for state-ofthe-art solvers and preconditioners. Alternatively, projection schemes or time-splitting methods
decouple equations for velocity and pressure, resulting in easier to solve linear systems. Although
pressure and velocity correction schemes of high-order accuracy are available for Newtonian
fluids, the extension to generalised Newtonian fluids is not a trivial task. Herein, we present
a split-step scheme based on an explicit-implicit treatment of pressure, viscosity and convection
terms, combined with a pressure Poisson equation with fully consistent boundary conditions.
Then, using standard equal-order finite elements becomes possible. Stability, flexibility and
efficiency of the splitting scheme is showcased in two challenging applications involving aortic
aneurysm flow and human phonation.The authors gratefully acknowledge Graz University of Technology for the financial support of the Lead-project: Mechanics, Modeling and Simulation of Aortic Dissection.Schussnig, R.; Pacheco, D.; Kaltenbacher, M.; Fries, T. (2022). Efficient and Higher-Order Accurate Split-Step Methods for Generalised Newtonian Fluid Flow. En Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference. Editorial Universitat Politècnica de València. 335-344. https://doi.org/10.4995/YIC2021.2021.12217OCS33534
On the Incorporation of Obstacles in a Fluid Flow Problem Using a Navier-Stokes-Brinkman Penalization Approach
Simulating the interaction of fluids with immersed moving solids is playing
an important role for gaining a better quantitative understanding of how fluid
dynamics is altered by the presence of obstacles and which forces are exerted
on the solids by the moving fluid. Such problems appear in various contexts,
ranging from numerous technical applications such as turbines to medical
problems such as the regulation of hemodyamics by valves. Typically, the
numerical treatment of such problems is posed within a fluid structure
interaction (FSI) framework. General FSI models are able to capture
bidirectional interactions, but are challenging to solve and computationally
expensive. Simplified methods offer a possible remedy by achieving better
computational efficiency to broaden the scope to demanding application problems
with focus on understanding the effect of solids on altering fluid dynamics. In
this study we report on the development of a novel method for such
applications. In our method rigid moving obstacles are incorporated in a fluid
dynamics context using concepts from porous media theory. Based on the
Navier-Stokes-Brinkman equations which augments the Navier-Stokes equation with
a Darcy drag term our method represents solid obstacles as time-varying regions
containing a porous medium of vanishing permeability. Numerical stabilization
and turbulence modeling is dealt with by using a residual based variational
multiscale formulation. The key advantages of our approach -- computational
efficiency and ease of implementation -- are demonstrated by solving a standard
benchmark problem of a rotating blood pump posed by the Food and Drug
Administration Agency (FDA). Validity is demonstrated by conducting a mesh
convergence study and by comparison against the extensive set of experimental
data provided for this benchmark
Semi-implicit fluid–structure interaction in biomedical applications
Fluid–structure interaction (FSI) incorporates effects of fluid flows on deformable solids and vice versa. Complex biomedical problems in clinical applications continue to challenge numerical algorithms, as incorporating the underlying mathematical methods can impair the solvers’ performance drastically. In this regard, we extend a semi-implicit, pressure Poisson-based FSI scheme for non-Newtonian fluids to incorporate several models crucial for biomechanical applications. We consider Windkessel outlets to account for neglected downstream flow regions, realistic material fibre orientation and stressed reference geometries reconstructed from medical image data. Additionally, we incorporate vital numerical aspects, namely, stabilisations to counteract dominant convective effects and instabilities triggered by re-entrant flow, while a major contribution of this work is combining interface quasi-Newton methods with Robin coupling conditions to accelerate the partitioned (semi-)implicit coupling scheme. The numerical examples presented herein aim to finally bridge the gap to real-world applications, considering state-of-the-art modelling aspects and physiological parameters. FSI simulations of blood flow in an iliac bifurcation derived from medical images and vocal folds deforming in the process of human phonation demonstrate the versatility of the framework
Numerical modelling of the Oldroyd-B fluid
The purpose of this thesis is to develop a 3D finite element model of the Oldroyd-B fluid for use in a complex geometry. The model is developed in deal.ii, which is a C++ finite element library. In addition to the standard finite element approach for the momentum equation, the discontinuous Galerkin method is used for the constitutive relation of the fluid model, with the extra stress as the unknown variable. The model developed is verified by using the symmetric “flow over a cylinder” benchmark problem. The effect of using piecewise-constant discontinuous and bilinear discontinuous elements for the extra stress field is investigated. The the results of the scheme are compared to those found in literature. The model is implemented in the solution of a complex problem of blood flow in an arteriovenous fistula, using geometry acquired from MRI data. A resistance boundary condition is used for the outlets. The flow profiles obtained from using both the Newtonian and Oldroyd-B fluids are validated against velocity encoded MRI and also compared to Fluid-Structure Interaction results for Newtonian fluids, from the literature. The effect of using a viscoelastic fluid on the flow profile and wall shear stresses are investigated. The results from this work show that using a viscoelastic fluid, rather than a Newtonian fluid, provides additional details regarding the wall shear stress in the arteriovenous fistula
Dynamic and fluid–structure interaction simulations of bioprosthetic heart valves using parametric design with T-splines and Fung-type material models
This paper builds on a recently developed immersogeometric fluid–structure interaction (FSI) methodology for bioprosthetic heart valve (BHV) modeling and simulation. It enhances the proposed framework in the areas of geometry design and constitutive modeling. With these enhancements, BHV FSI simulations may be performed with greater levels of automation, robustness and physical realism. In addition, the paper presents a comparison between FSI analysis and standalone structural dynamics simulation driven by prescribed transvalvular pressure, the latter being a more common modeling choice for this class of problems. The FSI computation achieved better physiological realism in predicting the valve leaflet deformation than its standalone structural dynamics counterpart
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