13,182 research outputs found
A geometric-based convection approach of 3-D reconstruction
Surface reconstruction algorithms produce piece-wise linear approximations of a surface S from a finite, sufficiently dense, subset of its points. In this paper, we present a fast algorithm for surface reconstruction from scattered data sets. This algorithm is inspired of an existing numerical convection scheme developed by Zhao, Osher and Fedkiw. Unlike this latter, the result of our algorithm does not depend on the precision of a (rectangular- ) grid. The reconstructed surface is simply a set of oriented faces located into the 3D Delaunay triangulation of the points. It is the result of the evolution of an oriented pseudo-surface. The representation of the evolving pseudo-surface uses an appropriate data structure together with operations that allow deformation and topological changes of it. The presented algorithm can handle complicated topologies and, unlike most of the others schemes, it involves no heuristic. The complexity of that method is that of the 3D Delaunay triangulation of the points. We present results of this algorithm which turned out to be efficient even in presence of noise
A quasinonlocal coupling method for nonlocal and local diffusion models
In this paper, we extend the idea of "geometric reconstruction" to couple a
nonlocal diffusion model directly with the classical local diffusion in one
dimensional space. This new coupling framework removes interfacial
inconsistency, ensures the flux balance, and satisfies energy conservation as
well as the maximum principle, whereas none of existing coupling methods for
nonlocal-to-local coupling satisfies all of these properties. We establish the
well-posedness and provide the stability analysis of the coupling method. We
investigate the difference to the local limiting problem in terms of the
nonlocal interaction range. Furthermore, we propose a first order finite
difference numerical discretization and perform several numerical tests to
confirm the theoretical findings. In particular, we show that the resulting
numerical result is free of artifacts near the boundary of the domain where a
classical local boundary condition is used, together with a coupled fully
nonlocal model in the interior of the domain
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Hydrodynamic Analysis of Binary Immiscible Metallurgical Flow in a Novel Mixing Process: Rheomixing
This paper presents a hydrodynamic analysis of binary immiscible metallurgical flow by a numerical simulation of the rheomixing process. The concept of multi-controll is proposed for classifying complex processes and identifying individual processes in an immiscible alloy system in order to perform simulations. A brief review of fabrication methods for immiscible alloys is given, and fluid flow aspects of a novel fabrication method – rheomixing by twin-screw extruder (TSE) are analysed. Fundamental hydrodynamic micro-mechanisms in a TSE are simulated by a piecewise linear (PLIC) volume-of-fluid (VOF) method coupled with the continuum surface force (CFS) algorithm. This revealed that continuous reorientation in the TSE process could produce fine droplets and the best mixing efficiency. It is verified that TSE is a better mixing device than single screw extruder (SSE) and can achieve finer droplets. Numerical results show good qualitative agreement with experimental results. It is concluded that rheomixing by a TSE can be successfully employed for casting immiscible engineering alloys due to its unique characteristics of reorientation and surface renewal
Koopman analysis of the long-term evolution in a turbulent convection cell
We analyse the long-time evolution of the three-dimensional flow in a closed
cubic turbulent Rayleigh-B\'{e}nard convection cell via a Koopman eigenfunction
analysis. A data-driven basis derived from diffusion kernels known in machine
learning is employed here to represent a regularized generator of the unitary
Koopman group in the sense of a Galerkin approximation. The resulting Koopman
eigenfunctions can be grouped into subsets in accordance with the discrete
symmetries in a cubic box. In particular, a projection of the velocity field
onto the first group of eigenfunctions reveals the four stable large-scale
circulation (LSC) states in the convection cell. We recapture the preferential
circulation rolls in diagonal corners and the short-term switching through roll
states parallel to the side faces which have also been seen in other
simulations and experiments. The diagonal macroscopic flow states can last as
long as a thousand convective free-fall time units. In addition, we find that
specific pairs of Koopman eigenfunctions in the secondary subset obey enhanced
oscillatory fluctuations for particular stable diagonal states of the LSC. The
corresponding velocity field structures, such as corner vortices and swirls in
the midplane, are also discussed via spatiotemporal reconstructions.Comment: 32 pages, 9 figures, article in press at Journal of Fluid Mechanic
An adaptive octree finite element method for PDEs posed on surfaces
The paper develops a finite element method for partial differential equations
posed on hypersurfaces in , . The method uses traces of
bulk finite element functions on a surface embedded in a volumetric domain. The
bulk finite element space is defined on an octree grid which is locally refined
or coarsened depending on error indicators and estimated values of the surface
curvatures. The cartesian structure of the bulk mesh leads to easy and
efficient adaptation process, while the trace finite element method makes
fitting the mesh to the surface unnecessary. The number of degrees of freedom
involved in computations is consistent with the two-dimension nature of surface
PDEs. No parametrization of the surface is required; it can be given implicitly
by a level set function. In practice, a variant of the marching cubes method is
used to recover the surface with the second order accuracy. We prove the
optimal order of accuracy for the trace finite element method in and
surface norms for a problem with smooth solution and quasi-uniform mesh
refinement. Experiments with less regular problems demonstrate optimal
convergence with respect to the number of degrees of freedom, if grid
adaptation is based on an appropriate error indicator. The paper shows results
of numerical experiments for a variety of geometries and problems, including
advection-diffusion equations on surfaces. Analysis and numerical results of
the paper suggest that combination of cartesian adaptive meshes and the
unfitted (trace) finite elements provide simple, efficient, and reliable tool
for numerical treatment of PDEs posed on surfaces
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