5,900 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
A numerical stabilization framework for viscoelastic fluid flow using the finite volume method on general unstructured meshes
A robust finite volume method for viscoelastic flow analysis on general
unstructured meshes is developed. It is built upon a general-purpose
stabilization framework for high Weissenberg number flows. The numerical
framework provides full combinatorial flexibility between different kinds of
rheological models on the one hand, and effective stabilization methods on the
other hand. A special emphasis is put on the velocity-stress-coupling on
co-located computational grids. Using special face interpolation techniques, a
semi-implicit stress interpolation correction is proposed to correct the
cell-face interpolation of the stress in the divergence operator of the
momentum balance. Investigating the entry-flow problem of the 4:1 contraction
benchmark, we demonstrate that the numerical methods are robust over a wide
range of Weissenberg numbers and significantly alleviate the high Weissenberg
number problem. The accuracy of the results is evaluated in a detailed mesh
convergence study
Bending models of lipid bilayer membranes: spontaneous curvature and area-difference elasticity
We preset a computational study of bending models for the curvature
elasticity of lipid bilayer membranes that are relevant for simulations of
vesicles and red blood cells. We compute bending energy and forces on
triangulated meshes and evaluate and extend four well established schemes for
their approximation: Kantor and Nelson 1987, Phys. Rev. A 36, 4020, J\"ulicher
1996, J. Phys. II France 6, 1797, Gompper and Kroll 1996, J. Phys. I France 6,
1305, and Meyer et. al. 2003 in Visualization and Mathematics III, Springer,
p35, termed A, B, C, D. We present a comparative study of these four schemes on
the minimal bending model and propose extensions for schemes B, C and D. These
extensions incorporate the reference state and non-local energy to account for
the spontaneous curvature, bilayer coupling, and area-difference elasticity
models. Our results indicate that the proposed extensions enhance the models to
account for shape transformation including budding/vesiculation as well as for
non-axisymmetric shapes. We find that the extended scheme B is superior to the
rest in terms of accuracy, and robustness as well as simplicity of
implementation. We demonstrate the capabilities of this scheme on several
benchmark problems including the budding-vesiculating process and the
reproduction of the phase diagram of vesicles
Surface-tension-driven Stokes flow: a numerical method based on conformal geometry
AbstractA novel numerical scheme is presented for solving the problem of two dimensional Stokes flows with free boundaries whose evolution is driven by surface tension. The formulation is based on a complex variable formulation of Stokes flow and use of conformal mapping to track the free boundaries. The method is motivated by applications to modelling the fabrication process for microstructured optical fibres (MOFs), also known as āholey fibresā, and is therefore tailored for the computation of multiple interacting free boundaries. We give evidence of the efficacy of the method and discuss its performance
A novel approach to rigid spheroid models in viscous flows using operator splitting methods
Calculating cost-effective solutions to particle dynamics in viscous flows is
an important problem in many areas of industry and nature. We implement a
second-order symmetric splitting method on the governing equations for a rigid
spheroidal particle model with torques, drag and gravity. The method splits the
operators into a vector field that is conservative and one that takes into
account the forces of the fluid. Error analysis and numerical tests are
performed on perturbed and stiff particle-fluid systems. For the perturbed
case, the splitting method greatly improves the solution accuracy, when
compared to a conventional multi-step method, and the global error behaves as
for roughly equal computational cost. For stiff
systems, we show that the splitting method retains stability in regimes where
conventional methods blow up. In addition, we show through numerical
experiments that the global order is reduced from
in the non-stiff regime to in
the stiff regime.Comment: 24 pages, 6 figures (13 if you count sub figs), all figures are in
colou
Using computational modelling to study extensional rheometry tests for inelastic fluids
The present work focuses on the extensional rheometry test, performed with the Sentmanat extensional rheometer (SER) device, and its main objectives are: (i) to establish the modelling
requirements, such as the geometry of the computational domain, initial and boundary conditions,
appropriate case setup, and (ii) to investigate the effect of self-induced errors, namely on the sample
dimensions and test temperature, on the extensional viscosity obtained through the extensional rheometry tests. The definition of the modelling setup also comprised the selection of the appropriate
mesh refinement level to model the process and the conclusion that gravity can be neglected without
affecting the numerical predictions. The subsequent study allowed us to conclude that the errors on
the sample dimensions have similar effects, originating differences on the extensional viscosity proportional to the induced variations. On the other hand, errors of a similar order of magnitude on
the test temperature promote a significant difference in the predicted extensional viscosity.This work was funded by FEDER funds through the COMPETE 2020 Program and National Funds through FCT-Portuguese Foundation for Science and Technology under the projects UIDB/05256/2020/, UIDP/05256/2020, CPCA/A2/6202/2020, CPCA_A2_6231_2020, NORTE-08-5369-
FSE-000034, under program IMPULSE-PolĆmeros e CompĆ³sitos: Drivers da InovaĆ§Ć£o TecnolĆ³gica e
da Competitividade Industrial
PAN AIR: A computer program for predicting subsonic or supersonic linear potential flows about arbitrary configurations using a higher order panel method. Volume 3: Case manual (version 1.0)
Numerous applications of the PAN AIR computer program system are presented. PAN AIR is user-oriented tool for analyzing and/or designing aerodynamic configurations in subsonic or supersonic flow using a technique generally referred to as a higher order panel method. Problems solved include simple wings in subsonic and supersonic flow, a wing-body in supersonic flow, wing with deflected flap in subsonic flow, design of two-dimensional and three-dimensional wings, axisymmetric nacelle in supersonic flow, and wing-canard-tail-nacelle-fuselage combination in supersonic flow
Bifurcations of piecewise smooth ļ¬ows:perspectives, methodologies and open problems
In this paper, the theory of bifurcations in piecewise smooth flows is critically surveyed. The focus is on results that hold in arbitrarily (but finitely) many dimensions, highlighting significant areas where a detailed understanding is presently lacking. The clearest results to date concern equilibria undergoing bifurcations at switching boundaries, and limit cycles undergoing grazing and sliding bifurcations. After discussing fundamental concepts, such as topological equivalence of two piecewise smooth systems, discontinuity-induced bifurcations are defined for equilibria and limit cycles. Conditions for equilibria to exist in n-dimensions are given, followed by the conditions under which they generically undergo codimension-one bifurcations. The extent of knowledge of their unfoldings is also summarized. Codimension-one bifurcations of limit cycles and boundary-intersection crossing are described together with techniques for their classification. Codimension-two bifurcations are discussed with suggestions for further study
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