50,949 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
Boost-Invariant (2+1)-dimensional Anisotropic Hydrodynamics
We present results of the application of the anisotropic hydrodynamics
(aHydro) framework to (2+1)-dimensional boost invariant systems. The necessary
aHydro dynamical equations are derived by taking moments of the Boltzmann
equation using a momentum-space anisotropic one-particle distribution function.
We present a derivation of the necessary equations and then proceed to
numerical solutions of the resulting partial differential equations using both
realistic smooth Glauber initial conditions and fluctuating Monte-Carlo Glauber
initial conditions. For this purpose we have developed two numerical
implementations: one which is based on straightforward integration of the
resulting partial differential equations supplemented by a two-dimensional
weighted Lax-Friedrichs smoothing in the case of fluctuating initial
conditions; and another that is based on the application of the Kurganov-Tadmor
central scheme. For our final results we compute the collective flow of the
matter via the lab-frame energy-momentum tensor eccentricity as a function of
the assumed shear viscosity to entropy ratio, proper time, and impact
parameter.Comment: 45 pages, 12 figures; v2 published versio
Robust Feature Detection and Local Classification for Surfaces Based on Moment Analysis
The stable local classification of discrete surfaces with respect to features such as edges and corners or concave and convex regions, respectively, is as quite difficult as well as indispensable for many surface processing applications. Usually, the feature detection is done via a local curvature analysis. If concerned with large triangular and irregular grids, e.g., generated via a marching cube algorithm, the detectors are tedious to treat and a robust classification is hard to achieve. Here, a local classification method on surfaces is presented which avoids the evaluation of discretized curvature quantities. Moreover, it provides an indicator for smoothness of a given discrete surface and comes together with a built-in multiscale. The proposed classification tool is based on local zero and first moments on the discrete surface. The corresponding integral quantities are stable to compute and they give less noisy results compared to discrete curvature quantities. The stencil width for the integration of the moments turns out to be the scale parameter. Prospective surface processing applications are the segmentation on surfaces, surface comparison, and matching and surface modeling. Here, a method for feature preserving fairing of surfaces is discussed to underline the applicability of the presented approach.
A Phase Field Model for Continuous Clustering on Vector Fields
A new method for the simplification of flow fields is presented. It is based on continuous clustering. A well-known physical clustering model, the Cahn Hilliard model, which describes phase separation, is modified to reflect the properties of the data to be visualized. Clusters are defined implicitly as connected components of the positivity set of a density function. An evolution equation for this function is obtained as a suitable gradient flow of an underlying anisotropic energy functional. Here, time serves as the scale parameter. The evolution is characterized by a successive coarsening of patterns-the actual clustering-during which the underlying simulation data specifies preferable pattern boundaries. We introduce specific physical quantities in the simulation to control the shape, orientation and distribution of the clusters as a function of the underlying flow field. In addition, the model is expanded, involving elastic effects. In the early stages of the evolution shear layer type representation of the flow field can thereby be generated, whereas, for later stages, the distribution of clusters can be influenced. Furthermore, we incorporate upwind ideas to give the clusters an oriented drop-shaped appearance. Here, we discuss the applicability of this new type of approach mainly for flow fields, where the cluster energy penalizes cross streamline boundaries. However, the method also carries provisions for other fields as well. The clusters can be displayed directly as a flow texture. Alternatively, the clusters can be visualized by iconic representations, which are positioned by using a skeletonization algorithm.
Adomain computation of radiative-convective bi-directional stretching flow of a magnetic non-Newtonian fluid in porous media with homogeneous-heterogeneous reactions
In the present communication, laminar, incompressible, hydromagnetic flow of
an electrically conducting non-Newtonian (Sisko) fluid over a bi-directional stretching sheet in
a porous medium is studied theoretically. Thermal radiation flux, homogeneous-heterogeneous
chemical reactions and convective wall heating are included in the model. Darcyâs model is
employed for the porous medium and Rosselandâs model for radiation heat transfer. The
governing partial differential equations for mass, momentum, energy and concentration are
reduced into ordinary differential equations via similarity transformations. The resultant
nonlinear ordinary differential equations with transformed boundary conditions are then solved
via the semi-analytical Adomain decomposition method (ADM). Validation with earlier studies
is included for the non-radiative case. Extensive visualization of velocity, temperature and
species concentration distributions for various emerging parameters is included. Increasing
magnetic field and inverse permeability parameter are observed to decelerate both the primary
and secondary velocity magnitudes whereas they increase temperatures in the regime.
Increasing sheet stretching ratio weakly accelerates the primary flow throughout the boundary
layer whereas it more dramatically accelerates the secondary flow near sheet surface.
Temperature is consistently reduced with increasing stretching sheet ratio whereas it is strongly
enhanced with greater radiative parameter. With greater Sisko non-Newtonian power-law
index the primary velocity and temperature are decreased whereas the secondary velocity is
increased. Increasing both homogenous and heterogenous chemical reaction parameters is
found to weakly and more strongly, respectively, deplete concentration magnitudes whereas
greater Schmidt number enhances them. Primary and secondary skin friction and Nusselt
number profiles are also computed. The study is relevant to electro-conductive (magnetic
polymer) materials processing operations
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