13,177 research outputs found
Consistent Computation of First- and Second-Order Differential Quantities for Surface Meshes
Differential quantities, including normals, curvatures, principal directions,
and associated matrices, play a fundamental role in geometric processing and
physics-based modeling. Computing these differential quantities consistently on
surface meshes is important and challenging, and some existing methods often
produce inconsistent results and require ad hoc fixes. In this paper, we show
that the computation of the gradient and Hessian of a height function provides
the foundation for consistently computing the differential quantities. We
derive simple, explicit formulas for the transformations between the first- and
second-order differential quantities (i.e., normal vector and principal
curvature tensor) of a smooth surface and the first- and second-order
derivatives (i.e., gradient and Hessian) of its corresponding height function.
We then investigate a general, flexible numerical framework to estimate the
derivatives of the height function based on local polynomial fittings
formulated as weighted least squares approximations. We also propose an
iterative fitting scheme to improve accuracy. This framework generalizes
polynomial fitting and addresses some of its accuracy and stability issues, as
demonstrated by our theoretical analysis as well as experimental results.Comment: 12 pages, 12 figures, ACM Solid and Physical Modeling Symposium, June
200
Simulation of inviscid compressible multi-phase flow with condensation
Condensation of vapours in rapid expansions of compressible gases is investigated. In the case of high temperature gradients the condensation will start at conditions well away from thermodynamic equilibrium of the fluid. In those cases homogeneous condensation is dominant over heterogeneous condensation. The present work is concerned with development of a simulation tool for computation of high speed compressible flows with homogeneous condensation. The resulting flow solver should preferably be accurate and robust to be used for simulation of industrial flows in general geometries
Physics Of Eclipsing Binaries. II. Towards the Increased Model Fidelity
The precision of photometric and spectroscopic observations has been
systematically improved in the last decade, mostly thanks to space-borne
photometric missions and ground-based spectrographs dedicated to finding
exoplanets. The field of eclipsing binary stars strongly benefited from this
development. Eclipsing binaries serve as critical tools for determining
fundamental stellar properties (masses, radii, temperatures and luminosities),
yet the models are not capable of reproducing observed data well either because
of the missing physics or because of insufficient precision. This led to a
predicament where radiative and dynamical effects, insofar buried in noise,
started showing up routinely in the data, but were not accounted for in the
models. PHOEBE (PHysics Of Eclipsing BinariEs; http://phoebe-project.org) is an
open source modeling code for computing theoretical light and radial velocity
curves that addresses both problems by incorporating missing physics and by
increasing the computational fidelity. In particular, we discuss triangulation
as a superior surface discretization algorithm, meshing of rotating single
stars, light time travel effect, advanced phase computation, volume
conservation in eccentric orbits, and improved computation of local intensity
across the stellar surfaces that includes photon-weighted mode, enhanced limb
darkening treatment, better reflection treatment and Doppler boosting. Here we
present the concepts on which PHOEBE is built on and proofs of concept that
demonstrate the increased model fidelity.Comment: 60 pages, 15 figures, published in ApJS; accompanied by the release
of PHOEBE 2.0 on http://phoebe-project.or
Adaptive mesh refinements for thin shells whose middle surface is not exactly known
A strategy concerning mesh refinements for thin shells computation is presented. The geometry of the shell is given only by the reduced information consisting in nodes and normals on its middle surface corresponding to a coarse mesh. The new point is that the mesh refinements are defined from several criteria, including the transverse shear forces which do not appear in the mechanical energy of the applied shell formulation. Another important point is to be able to construct the unknown middle surface at each step of the refinement. For this, an interpolation method by edges, coupled with a triangle bisection algorithm, is applied. This strategy is illustrated on various geometries and mechanical problems
Subdivision Directional Fields
We present a novel linear subdivision scheme for face-based tangent
directional fields on triangle meshes. Our subdivision scheme is based on a
novel coordinate-free representation of directional fields as halfedge-based
scalar quantities, bridging the finite-element representation with discrete
exterior calculus. By commuting with differential operators, our subdivision is
structure-preserving: it reproduces curl-free fields precisely, and reproduces
divergence-free fields in the weak sense. Moreover, our subdivision scheme
directly extends to directional fields with several vectors per face by working
on the branched covering space. Finally, we demonstrate how our scheme can be
applied to directional-field design, advection, and robust earth mover's
distance computation, for efficient and robust computation
An Entropy Stable Nodal Discontinuous Galerkin Method for the Two Dimensional Shallow Water Equations on Unstructured Curvilinear Meshes with Discontinuous Bathymetry
We design an arbitrary high-order accurate nodal discontinuous Galerkin
spectral element approximation for the nonlinear two dimensional shallow water
equations with non-constant, possibly discontinuous, bathymetry on
unstructured, possibly curved, quadrilateral meshes. The scheme is derived from
an equivalent flux differencing formulation of the split form of the equations.
We prove that this discretisation exactly preserves the local mass and
momentum. Furthermore, combined with a special numerical interface flux
function, the method exactly preserves the mathematical entropy, which is the
total energy for the shallow water equations. By adding a specific form of
interface dissipation to the baseline entropy conserving scheme we create a
provably entropy stable scheme. That is, the numerical scheme discretely
satisfies the second law of thermodynamics. Finally, with a particular
discretisation of the bathymetry source term we prove that the numerical
approximation is well-balanced. We provide numerical examples that verify the
theoretical findings and furthermore provide an application of the scheme for a
partial break of a curved dam test problem
A Nitsche-based cut finite element method for a fluid--structure interaction problem
We present a new composite mesh finite element method for fluid--structure
interaction problems. The method is based on surrounding the structure by a
boundary-fitted fluid mesh which is embedded into a fixed background fluid
mesh. The embedding allows for an arbitrary overlap of the fluid meshes. The
coupling between the embedded and background fluid meshes is enforced using a
stabilized Nitsche formulation which allows us to establish stability and
optimal order \emph{a priori} error estimates,
see~\cite{MassingLarsonLoggEtAl2013}. We consider here a steady state
fluid--structure interaction problem where a hyperelastic structure interacts
with a viscous fluid modeled by the Stokes equations. We evaluate an iterative
solution procedure based on splitting and present three-dimensional numerical
examples.Comment: Revised version, 18 pages, 7 figures. Accepted for publication in
CAMCo
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