1,080 research outputs found
The LifeV library: engineering mathematics beyond the proof of concept
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.Comment: Review of the LifeV Finite Element librar
Numerical simulation of steady supersonic flow
A noniterative, implicit, space-marching, finite-difference algorithm was developed for the steady thin-layer Navier-Stokes equations in conservation-law form. The numerical algorithm is applicable to steady supersonic viscous flow over bodies of arbitrary shape. In addition, the same code can be used to compute supersonic inviscid flow or three-dimensional boundary layers. Computed results from two-dimensional and three-dimensional versions of the numerical algorithm are in good agreement with those obtained from more costly time-marching techniques
Pattern fluctuations in transitional plane Couette flow
In wide enough systems, plane Couette flow, the flow established between two
parallel plates translating in opposite directions, displays alternatively
turbulent and laminar oblique bands in a given range of Reynolds numbers R. We
show that in periodic domains that contain a few bands, for given values of R
and size, the orientation and the wavelength of this pattern can fluctuate in
time. A procedure is defined to detect well-oriented episodes and to determine
the statistics of their lifetimes. The latter turn out to be distributed
according to exponentially decreasing laws. This statistics is interpreted in
terms of an activated process described by a Langevin equation whose
deterministic part is a standard Landau model for two interacting complex
amplitudes whereas the noise arises from the turbulent background.Comment: 13 pages, 11 figures. Accepted for publication in Journal of
statistical physic
Decoupling methods for the time-dependent Navier-Stokes-Darcy interface model
In this research, several decoupling methods are developed and analyzed for approximating the solution of time-dependent Navier-Stokes-Darcy (NS-Darcy) interface problems. This research on decoupling methods is motivated to efficiently solve the complex Stokes-Darcy or NS-Darcy type models, which arise from many interesting real world problems involved with or even dominated by the coupled porous media flow and free flow. We first discuss a semi-implicit, multi-step non-iterative domain decomposition (NIDDM) to solve a coupled unsteady NS-Darcy system with Beavers-Joseph-Saffman-Jones (BJSJ) interface condition and obtain optimal error estimates. Second, a parallel NIDDM is developed to solve unsteady NS-Darcy model with Beavers-Joseph (BJ) interface condition, which is much more complicated than BJSJ interface condition. We overcome the major difficulties in the analysis which arise from nonlinear terms and BJ interface condition. Furthermore, a Lagrange multiplier method is proposed under the framework of the domain decomposition method to overcome the difficulty of non-unique solutions arising from the defective boundary condition. Meanwhile, we propose and analyze an efficient ensemble algorithm, which can significantly improve the computational efficiency, for fast computation of multiple realizations of the stochastic Stokes-Darcy model with a random hydraulic conductivity tensor. Furthermore, we utilize the idea of artificial compressibility, which decouples the velocity and pressure, to construct the decoupled ensemble algorithm to improve computational efficiency further. We prove that the proposed ensemble methods offer long time stability and optimal error estimates under a time-step condition and two parameter conditions --Abstract, page iii
Computational methods in cardiovascular mechanics
The introduction of computational models in cardiovascular sciences has been
progressively bringing new and unique tools for the investigation of the
physiopathology. Together with the dramatic improvement of imaging and
measuring devices on one side, and of computational architectures on the other
one, mathematical and numerical models have provided a new, clearly
noninvasive, approach for understanding not only basic mechanisms but also
patient-specific conditions, and for supporting the design and the development
of new therapeutic options. The terminology in silico is, nowadays, commonly
accepted for indicating this new source of knowledge added to traditional in
vitro and in vivo investigations. The advantages of in silico methodologies are
basically the low cost in terms of infrastructures and facilities, the reduced
invasiveness and, in general, the intrinsic predictive capabilities based on
the use of mathematical models. The disadvantages are generally identified in
the distance between the real cases and their virtual counterpart required by
the conceptual modeling that can be detrimental for the reliability of
numerical simulations.Comment: 54 pages, Book Chapte
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