152 research outputs found
Cumulative reports and publications through 31 December 1983
All reports for the calendar years 1975 through December 1983 are listed by author. Since ICASE reports are intended to be preprints of articles for journals and conference proceedings, the published reference is included when available. Thirteen older journal and conference proceedings references are included as well as five additional reports by ICASE personnel. Major categories of research covered include: (1) numerical methods, with particular emphasis on the development and analysis of basic algorithms; (2) computational problems in engineering and the physical sciences, particularly fluid dynamics, acoustics, structural analysis, and chemistry; and (3) computer systems and software, especially vector and parallel computers, microcomputers, and data management
A multi-domain implementation of the pseudo-spectral method and compact finite difference schemes for solving time-dependent differential equations
Abstract : In this dissertation, we introduce new numerical methods for solving time-dependant differential equations. These methods involve dividing the domain of the problem into multiple sub domains. The nonlinearity of the differential equations is dealt with by using a Gauss-Seidel like relaxation or quasilinearisation technique. To solve the linearized iteration schemes obtained we use either higher order compact finite difference schemes or spectral collocation methods and we call the resulting methods the multi-domain compact finite difference relaxation method (MD-CFDRM), multi-domain compact finite difference quasilinearisation method (MD-CFDQLM) and multi-domain bivariate spectral quasilinearisation method (MD-BSQLM) respectively. We test the applicability of these methods in a wide variety of differential equations. The accuracy is compared against other methods as well as other results from literature. The MD-CFDRM is used to solve famous chaotic systems and hyperchaotic systems. Chaotic and hyperchaotic systems are characterized by high sensitivity to small perturbation on initial data and rapidly changing solutions. Such rapid variations in the solution pose tremendous problems to a number of numerical approximations. We modify the CFDs to be able to deal with such systems of equations. We also used the MD-CFDQLM to solve the nonlinear evolution partial differential equations, namely, the Fisher’s equation, Burgers- Fisher equation, Burgers-Huxley equation and the coupled Burgers’ equations over a large time domain. The main advantage of this approach is that it offers better accuracy on coarser grids which significantly improves the computational speed of the method for large time domain. We also studied the generalized Kuramoto-Sivashinsky (GKS) equations. The KS equations exhibit chaotic behaviour under certain conditions. We used the multi-domain bivariate spectral quasilinearisation method (MD-BSQLM) to approximate the numerical solutions for the generalized KS equations.M.Sc. (Pure and Applied Mathematics
Cumulative reports and publications thru 31 December 1982
Institute for Computer Applications in Science and Engineering (ICASE) reports are documented
Tracking Vector Magnetograms with the Magnetic Induction Equation
The differential affine velocity estimator (DAVE) developed in Schuck (2006)
for estimating velocities from line-of-sight magnetograms is modified to
directly incorporate horizontal magnetic fields to produce a differential
affine velocity estimator for vector magnetograms (DAVE4VM). The DAVE4VM's
performance is demonstrated on the synthetic data from the anelastic
pseudospectral ANMHD simulations that were used in the recent comparison of
velocity inversion techniques by Welsch (2007). The DAVE4VM predicts roughly
95% of the helicity rate and 75% of the power transmitted through the
simulation slice. Inter-comparison between DAVE4VM and DAVE and further
analysis of the DAVE method demonstrates that line-of-sight tracking methods
capture the shearing motion of magnetic footpoints but are insensitive to flux
emergence -- the velocities determined from line-of-sight methods are more
consistent with horizontal plasma velocities than with flux transport
velocities. These results suggest that previous studies that rely on velocities
determined from line-of-sight methods such as the DAVE or local correlation
tracking may substantially misrepresent the total helicity rates and power
through the photosphere.Comment: 30 pages, 13 figure
Cumulative reports and publications through December 31, 1990
This document contains a complete list of ICASE reports. Since ICASE reports are intended to be preprints of articles that will appear in journals or conference proceedings, the published reference is included when it is available
Cumulative reports and publications through December 31, 1988
This document contains a complete list of ICASE Reports. Since ICASE Reports are intended to be preprints of articles that will appear in journals or conference proceedings, the published reference is included when it is available
Deformation statistics of sub-Kolmogorov-scale ellipsoidal neutrally buoyant drops in isotropic turbulence
Small droplets in turbulent flows can undergo highly variable deformations
and orientational dynamics. For neutrally buoyant droplets smaller than the
Kolmogorov scale, the dominant effects from the surrounding turbulent flow
arise through Lagrangian time histories of the velocity gradient tensor. Here
we study the evolution of representative droplets using a model that includes
rotation and stretching effects from the surrounding fluid, and restoration
effects from surface tension including a constant droplet volume constraint,
while assuming that the droplets maintain an ellipsoidal shape. The model is
combined with Lagrangian time histories of the velocity gradient tensor
extracted from DNS of turbulence to obtain simulated droplet evolutions. These
are used to characterize the size, shape and orientation statistics of small
droplets in turbulence. A critical capillary number, is identified
associated with unbounded growth of one or two of the droplet's semi-axes.
Exploiting analogies with dynamics of polymers in turbulence, the number
can be predicted based on the large deviation theory for the largest Finite
Time Lyapunov exponent. Also, for sub-critical the theory enables
predictions of the slope of the power-law tails of droplet size distributions
in turbulence. For cases when the viscosities of droplet and outer fluid differ
in a way that enables vorticity to decorrelate the shape from the straining
directions, the large deviation formalism based on the stretching properties of
the velocity gradient tensor loses validity and its predictions fail. Even
considering the limitations of the assumed ellipsoidal droplet shape, the
results highlight the complex coupling between droplet deformation, orientation
and the local fluid velocity gradient tensor to be expected when small viscous
drops interact with turbulent flows
Cumulative reports and publications
A complete list of Institute for Computer Applications in Science and Engineering (ICASE) reports are listed. Since ICASE reports are intended to be preprints of articles that will appear in journals or conference proceedings, the published reference is included when it is available. The major categories of the current ICASE research program are: applied and numerical mathematics, including numerical analysis and algorithm development; theoretical and computational research in fluid mechanics in selected areas of interest to LaRC, including acoustics and combustion; experimental research in transition and turbulence and aerodynamics involving LaRC facilities and scientists; and computer science
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