91,092 research outputs found
Average Interpolation Under the Maximum Angle Condition
Interpolation error estimates needed in common finite element applications
using simplicial meshes typically impose restrictions on the both the
smoothness of the interpolated functions and the shape of the simplices. While
the simplest theory can be generalized to admit less smooth functions (e.g.,
functions in H^1(\Omega) rather than H^2(\Omega)) and more general shapes
(e.g., the maximum angle condition rather than the minimum angle condition),
existing theory does not allow these extensions to be performed simultaneously.
By localizing over a well-shaped auxiliary spatial partition, error estimates
are established under minimal function smoothness and mesh regularity. This
construction is especially important in two cases: L^p(\Omega) estimates for
data in W^{1,p}(\Omega) hold for meshes without any restrictions on simplex
shape, and W^{1,p}(\Omega) estimates for data in W^{2,p}(\Omega) hold under a
generalization of the maximum angle condition which previously required p>2 for
standard Lagrange interpolation
Using the generalized interpolation material point method for fluid-solid interactions induced by surface tension
This thesis is devoted to the development of new, Generalized Interpolation Material Point Method (GIMP)-based algorithms for handling surface tension and contact (wetting) in fluid-solid interaction (FSI) problems at small scales. In these problems, surface tension becomes so dominant that its influence on both fluids and solids must be considered. Since analytical solutions for most engineering problems are usually unavailable, numerical methods are needed to describe and predict complicated time-dependent states in the solid and fluid involved due to surface tension effects. Traditional computational methods for handling fluid-solid interactions may not be effective due to their weakness in solving large-deformation problems and the complicated coupling of two different types of computational frameworks: one for solid, and the other for fluid. On the contrary, GIMP, a mesh-free algorithm for solid mechanics problems, is numerically effective in handling problems involving large deformations and fracture. Here we extend the capability of GIMP to handle fluid dynamics problems with surface tension, and to develop a new contact algorithm to deal with the wetting boundary conditions that include the modeling of contact angle and slip near the triple points where the three phases -- fluid, solid, and vapor -- meet. The error of the new GIMP algorithm for FSI problems at small scales, as verified by various benchmark problems, generally falls within the 5% range. In this thesis, we have successfully extended the capability of GIMP for handling FSI problems under surface tension in a one-solver numerical framework, a unique and innovative approach.Chapter 1. Introduction -- Chapter 2. Using the generalized interpolation material point method for fluid dynamics at low reynolds numbers -- Chapter 3. On the modeling of surface tension and its applications by the generalized interpolation material point method -- Chapter 4. Using the generalized interpolation material point method for fluid-solid interactions induced by surface tension -- Chapter 5. Conclusions
Recommended from our members
Evaluation by simulation of interpolation and acceleration algorithms for Stepper Motors
Stepper motors are used to control CNC machines for many applications. As well as following the required path precisely, it is also important that the motion be smooth and that the surface speed be controllable. Improved interpolation algorithms for individual straight lines and circular arcs have been developed using distance as a parameter [Chow et al, 2002], [Chow, 2003]. The algorithms control the motor by means of pulses and the generation of the pulse timings is based on the geometry of the shape. For high speeds it is necessary to allow smooth acceleration at the beginning and similar smooth deceleration at the end. Thus, appropriate acceleration and deceleration algorithms have been developed for use with the new interpolation algorithms. This paper describes how simulation has been used to evaluate the new algorithms and compare them with previous algorithms. The algorithms are described for the 2D case but the principle can be extended to 3D
Cyclotron resonant scattering feature simulations. I. Thermally averaged cyclotron scattering cross sections, mean free photon-path tables, and electron momentum sampling
Electron cyclotron resonant scattering features (CRSFs) are observed as
absorption-like lines in the spectra of X-ray pulsars. A significant fraction
of the computing time for Monte Carlo simulations of these quantum mechanical
features is spent on the calculation of the mean free path for each individual
photon before scattering, since it involves a complex numerical integration
over the scattering cross section and the (thermal) velocity distribution of
the scattering electrons.
We aim to numerically calculate interpolation tables which can be used in
CRSF simulations to sample the mean free path of the scattering photon and the
momentum of the scattering electron. The tables also contain all the
information required for sampling the scattering electron's final spin.
The tables were calculated using an adaptive Simpson integration scheme. The
energy and angle grids were refined until a prescribed accuracy is reached. The
tables are used by our simulation code to produce artificial CRSF spectra. The
electron momenta sampled during these simulations were analyzed and justified
using theoretically determined boundaries.
We present a complete set of tables suited for mean free path calculations of
Monte Carlo simulations of the cyclotron scattering process for conditions
expected in typical X-ray pulsar accretion columns (0.01<B/B_{crit}<=0.12,
where B_{crit}=4.413x10^{13} G and 3keV<=kT<15keV). The sampling of the tables
is chosen such that the results have an estimated relative error of at most
1/15 for all points in the grid. The tables are available online at
http://www.sternwarte.uni-erlangen.de/research/cyclo.Comment: A&A, in pres
Evaluating the Differences of Gridding Techniques for Digital Elevation Models Generation and Their Influence on the Modeling of Stony Debris Flows Routing: A Case Study From Rovina di Cancia Basin (North-Eastern Italian Alps)
Debris \ufb02ows are among the most hazardous phenomena in mountain areas. To cope
with debris \ufb02ow hazard, it is common to delineate the risk-prone areas through
routing models. The most important input to debris \ufb02ow routing models are the
topographic data, usually in the form of Digital Elevation Models (DEMs). The quality
of DEMs depends on the accuracy, density, and spatial distribution of the sampled
points; on the characteristics of the surface; and on the applied gridding methodology.
Therefore, the choice of the interpolation method affects the realistic representation
of the channel and fan morphology, and thus potentially the debris \ufb02ow routing
modeling outcomes. In this paper, we initially investigate the performance of common
interpolation methods (i.e., linear triangulation, natural neighbor, nearest neighbor,
Inverse Distance to a Power, ANUDEM, Radial Basis Functions, and ordinary kriging)
in building DEMs with the complex topography of a debris \ufb02ow channel located
in the Venetian Dolomites (North-eastern Italian Alps), by using small footprint full-
waveform Light Detection And Ranging (LiDAR) data. The investigation is carried
out through a combination of statistical analysis of vertical accuracy, algorithm
robustness, and spatial clustering of vertical errors, and multi-criteria shape reliability
assessment. After that, we examine the in\ufb02uence of the tested interpolation algorithms
on the performance of a Geographic Information System (GIS)-based cell model for
simulating stony debris \ufb02ows routing. In detail, we investigate both the correlation
between the DEMs heights uncertainty resulting from the gridding procedure and
that on the corresponding simulated erosion/deposition depths, both the effect of
interpolation algorithms on simulated areas, erosion and deposition volumes, solid-liquid
discharges, and channel morphology after the event. The comparison among the tested
interpolation methods highlights that the ANUDEM and ordinary kriging algorithms
are not suitable for building DEMs with complex topography. Conversely, the linear
triangulation, the natural neighbor algorithm, and the thin-plate spline plus tension and completely regularized spline functions ensure the best trade-off among accuracy
and shape reliability. Anyway, the evaluation of the effects of gridding techniques on
debris \ufb02ow routing modeling reveals that the choice of the interpolation algorithm does
not signi\ufb01cantly affect the model outcomes
The implementation of the vegter yield criterion and a physically based hardening rule in finite elements
A new material description for sheet metal forming using Finite Elements has been developed. The description consists of a yield criterion and a hardening rule. In contrast to most former criteria the new criterion is based on multi-axial stress states. The yield criterion is extended with a physically based hardening rule, in which the flow stress depends on the strain and strain rate. A Limiting Dome Height test is used to examine the material description
- âŠ