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Accurate and effective methods for the numerical solution of incompressible fluid dynamics is an old but still important challenging problem, as more and more complex problems in engineering biology, ecology, medicine, sport are tackled with computational methods.
In this thesis, we investigate efficient solvers for two important models that gover...
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Cartesian grids represent a special extent in unstructured grid literature. They employ chiefly created algorithms to produce automatic meshing while simulating flows around complex geometries without considering shape of the bodies. In this article, firstly, it is intended to produce regionally developed Cartesian meshes for two
dimensional and th...
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... In particular, the Yosida scheme has been preferred since the error on the mass conservation has less impact on the interface with the structure in fluid-structure interaction problems. It is worth noting that a special block operator structure reflecting the algebraic factorization concept has been implemented in Villa [2011]. ...
LifeV is a library for the finite element (FE) solution of partial differential equations in one, two, and three dimensions. It is written in C++ and designed to run on diverse parallel architectures, including cloud and high performance computing facilities. In spite of its academic research nature, meaning a library for the development and testing of new methods, one distinguishing feature of LifeV is its use on real world problems and it is intended to provide a tool for many engineering applications. It has been actually used in computational hemodynamics, including cardiac mechanics and fluid-structure interaction problems, in porous media, ice sheets dynamics for both forward and inverse problems. In this paper we give a short overview of the features of LifeV and its coding paradigms on simple problems. The main focus is on the parallel environment which is mainly driven by domain decomposition methods and based on external libraries such as MPI, the Trilinos project, HDF5 and ParMetis. Dedicated to the memory of Fausto Saleri.
... We want to point out that the required time for one time step heavily depends on, in particular, the Reynolds number of the problem (and associated stabilization strategies), the size of the elements, the time stepping, the polynomial order used to approximate the various fields, and, obviously, the time integration schemes and the iterative solver technique. The interested readers may read 26 , and the literature cited therein, in particular 25 . Regarding the boundary conditions, the inflow flux has been obtain from the same patient from phase contrast Magnetic Resonance Imaging. ...
In the last 20 years, a new approach has emerged to investigate the physiopathology of circulation. By merging medical images with validated numerical models, it is possible to support doctors’ decision-making process. The iCardioCloud project aims at establishing a computational framework to perform a complete patient-specific numerical analysis, specially oriented to aortic diseases (like dissections or aneurysms) and to deliver a compelling synthesis. The project can be considered a pioneering example of a Computer Aided Clinical Trial: i.e., a comprehensive analysis of patients where the level of knowledge extracted by traditional measures and statistics is enhanced through the massive use of numerical modeling. From a computer engineering point of view, iCardioCloud faces multiple challenges. First, the number of problems to solve for each patient is significantly huge – this is typical of computational fluid dynamics (CFD) – and it requires parallel methods. In addition, working in a clinical environment demands efficiency as the timeline requires rapid quantitative answers (as may happen in an emergency scenario). It is therefore mandatory to employ high-end parallel systems, such as large clusters or supercomputers.
Here we discuss a parallel implementation of an application within the iCardioCloud project, built with a black-box approach – i.e., by assembling and configuring existing packages and libraries and in particular LifeV, a finite element library developed to solve CFD problems. The goal of this paper is to describe the software architecture underlying LifeV and to assess its performance and the most appropriate parallel paradigm.
This paper is an extension of a previous work presented at the PBio 2015 Conference. This revision extends the description of the software architecture and discusses several new serial and parallel optimizations to the application. We discuss the introduction of hybrid parallelism in order to mitigate some performance problems previously experienced.
... a parallel Finite Element solver. As for the applied numerical scheme, the time integration was performed using a second order BDF scheme with an algebraic splitting of the velocity and pressure fields with a Yosida scheme with pressure corrections [21,22]. The convective effects were treated using a Streamline Diffusion approach [23]. ...
Thoracic endovascular repair (TEVAR) is a minimally invasive alternative to classical open-chest surgery for pathologies of thoracic aorta such as aneurysms or dissections. It consists of the deployment of one or more endografts to either exclude aneurysms pressurization or seal entry tears of dissection. It is a minimally invasive procedure, yet long-term efficacy is still to be demonstrated and analyzed, depending on the geometry and the consequent hemodynamics and remodeling induced by the intervention. In this paper we consider a TEVAR patient by an extensive computational analysis of pre-op, post-op, and one-year follow up data. We focus on both geometrical features like curvature, torsion and area variations, as well as near-wall and intravascular flow-related quantities (i.e., wall shear stress-based descriptors and helicity). Comparison of the different morphologies indicates a partial restoration of normal flow in the region of interest, even though low WSS are still present with the associated risks. Overall, this study demonstrates the efficacy of quantitative computational tools in understanding the long-term impact of TEVAR.
... . We can rewrite (6)-(7) in the form (8) where (9) At every time level t n+1 , to solve system (8) we use the left preconditioned GMRES method. As preconditioner, we use an upper-triangular variant of the pressure corrected Yosida splitting [23,39] given by (10) The above preconditioner is a suitable approximation of the U factor in the exact block LU factorization of matrix A in (9): (11) See also [40,41,42,43] for more details. ...
We discuss in this paper the validation of an open source framework for the solution of problems arising in hemodynamics. The proposed framework is assessed through experimental data for fluid flow in an idealized medical device with rigid boundaries and a numerical benchmark for flow in compliant vessels. The core of the framework is an open source parallel finite element library that features several algorithms to solve both fluid and fluid-structure interaction problems. The numerical results for the flow in the idealized medical device (consisting of a conical convergent, a narrow throat, and a sudden expansion) are in good quantitative agreement with the measured axial components of the velocity and pressures for three different flow rates corresponding to laminar, transitional, and turbulent regimes. We emphasize the crucial role played by the accuracy in performing numerical integration, mesh, and time step to match the measurements. The numerical fluid-structure interaction benchmark deals with the propagation of a pressure wave in a fluid-filled elastic tube. The computed pressure wave speed and frequency of oscillations, and the axial velocity of the fluid on the tube axis are close to the values predicted by the analytical solution associated with the benchmark. A detailed account of the methods used for both benchmarks is provided.Copyright © 2013 John Wiley & Sons, Ltd.
... In addition to well known domain decomposition preconditioners, provided by the Trilinos libraries, LifeV contains for example a set of preconditioners designed for Navier-Stokes problems [76], [77], with an approach based on an approximate block factorization of the Navier-Stokes system matrix, and others for fluid-structure interaction problems [78]. ...
We describe in this paper an open source framework for the solution of problems arising in hemodynamics. The proposed framework is validated through comparison against experimental data for fluid flow in an idealized medical device with rigid boundaries; and verified with a numerical benchmark for flow in compliant vessels. The core of the framework is an open source parallel finite element library that features algorithms to solve both fluid and fluid-structure interaction problems. The computed results are in good quantitative agreement with experimental measurements and theoretical estimates.
We address a time-adaptive solver specifically devised for the incompressible Navier–Stokes (INS) equations. One of the challenging issues in this context is the identification of a reliable a posteriori error estimator. Typical strategies are based on the combination of the solutions computed either with two different time steps or two schemes with different accuracy. In this paper, we move from the pressure correction algebraic factorizations formerly proposed by Saleri, Veneziani (2005). These schemes feature an intrinsic hierarchical nature, such that an accurate solution for the pressure is obtained by computing intermediate low-order guesses. The difference between the two estimates provide a natural a posteriori estimator. After introducing the incremental formulation of the pressure correction schemes, we address the properties of this approach, including extensive implementation details. Numerical results presented refer to 2D and 3D unstructured problems, with a particular emphasis on cardiovascular problems, which are expected to largely benefit from time-adaptive solvers. In memory of F. Saleri (1965–2007).
