23,607 research outputs found
Fourth-order flows in surface modelling
This short article is a brief account of the usage of fourth-order curvature
flow in surface modelling
Wall Orientation and Shear Stress in the Lattice Boltzmann Model
The wall shear stress is a quantity of profound importance for clinical
diagnosis of artery diseases. The lattice Boltzmann is an easily parallelizable
numerical method of solving the flow problems, but it suffers from errors of
the velocity field near the boundaries which leads to errors in the wall shear
stress and normal vectors computed from the velocity. In this work we present a
simple formula to calculate the wall shear stress in the lattice Boltzmann
model and propose to compute wall normals, which are necessary to compute the
wall shear stress, by taking the weighted mean over boundary facets lying in a
vicinity of a wall element. We carry out several tests and observe an increase
of accuracy of computed normal vectors over other methods in two and three
dimensions. Using the scheme we compute the wall shear stress in an inclined
and bent channel fluid flow and show a minor influence of the normal on the
numerical error, implying that that the main error arises due to a corrupted
velocity field near the staircase boundary. Finally, we calculate the wall
shear stress in the human abdominal aorta in steady conditions using our method
and compare the results with a standard finite volume solver and experimental
data available in the literature. Applications of our ideas in a simplified
protocol for data preprocessing in medical applications are discussed.Comment: 9 pages, 11 figure
Mini-Workshop: Analytical and Numerical Methods in Image and Surface Processing
The workshop successfully brought together researchers from mathematical analysis, numerical mathematics, computer graphics and image processing. The focus was on variational methods in image and surface processing such as active contour models, Mumford-Shah type functionals, image and surface denoising based on geometric evolution problems in image and surface fairing, physical modeling of surfaces, the restoration of images and surfaces using higher order variational formulations
Spectral/hp element methods: recent developments, applications, and perspectives
The spectral/hp element method combines the geometric flexibility of the
classical h-type finite element technique with the desirable numerical
properties of spectral methods, employing high-degree piecewise polynomial
basis functions on coarse finite element-type meshes. The spatial approximation
is based upon orthogonal polynomials, such as Legendre or Chebychev
polynomials, modified to accommodate C0-continuous expansions. Computationally
and theoretically, by increasing the polynomial order p, high-precision
solutions and fast convergence can be obtained and, in particular, under
certain regularity assumptions an exponential reduction in approximation error
between numerical and exact solutions can be achieved. This method has now been
applied in many simulation studies of both fundamental and practical
engineering flows. This paper briefly describes the formulation of the
spectral/hp element method and provides an overview of its application to
computational fluid dynamics. In particular, it focuses on the use the
spectral/hp element method in transitional flows and ocean engineering.
Finally, some of the major challenges to be overcome in order to use the
spectral/hp element method in more complex science and engineering applications
are discussed
Implicit High-Order Flux Reconstruction Solver for High-Speed Compressible Flows
The present paper addresses the development and implementation of the first
high-order Flux Reconstruction (FR) solver for high-speed flows within the
open-source COOLFluiD (Computational Object-Oriented Libraries for Fluid
Dynamics) platform. The resulting solver is fully implicit and able to simulate
compressible flow problems governed by either the Euler or the Navier-Stokes
equations in two and three dimensions. Furthermore, it can run in parallel on
multiple CPU-cores and is designed to handle unstructured grids consisting of
both straight and curved edged quadrilateral or hexahedral elements. While most
of the implementation relies on state-of-the-art FR algorithms, an improved and
more case-independent shock capturing scheme has been developed in order to
tackle the first viscous hypersonic simulations using the FR method. Extensive
verification of the FR solver has been performed through the use of
reproducible benchmark test cases with flow speeds ranging from subsonic to
hypersonic, up to Mach 17.6. The obtained results have been favorably compared
to those available in literature. Furthermore, so-called super-accuracy is
retrieved for certain cases when solving the Euler equations. The strengths of
the FR solver in terms of computational accuracy per degree of freedom are also
illustrated. Finally, the influence of the characterizing parameters of the FR
method as well as the the influence of the novel shock capturing scheme on the
accuracy of the developed solver is discussed
Colliding Interfaces in Old and New Diffuse-interface Approximations of Willmore-flow
This paper is concerned with diffuse-interface approximations of the Willmore
flow. We first present numerical results of standard diffuse-interface models
for colliding one dimensional interfaces. In such a scenario evolutions towards
interfaces with corners can occur that do not necessarily describe the adequate
sharp-interface dynamics.
We therefore propose and investigate alternative diffuse-interface
approximations that lead to a different and more regular behavior if interfaces
collide. These dynamics are derived from approximate energies that converge to
the -lower-semicontinuous envelope of the Willmore energy, which is in
general not true for the more standard Willmore approximation
Multilevel Solvers for Unstructured Surface Meshes
Parameterization of unstructured surface meshes is of fundamental importance in many applications of digital geometry processing. Such parameterization approaches give rise to large and exceedingly ill-conditioned systems which are difficult or impossible to solve without the use of sophisticated multilevel preconditioning strategies. Since the underlying meshes are very fine to begin with, such multilevel preconditioners require mesh coarsening to build an appropriate hierarchy. In this paper we consider several strategies for the construction of hierarchies using ideas from mesh simplification algorithms used in the computer graphics literature. We introduce two novel hierarchy construction schemes and demonstrate their superior performance when used in conjunction with a multigrid preconditioner
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