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At least 829 records · Page 46

Models of thermal relaxation mechanics for particle simulation methods

A comparative study is conducted of the simulation of molecular vibrational relaxation in rarefied flows by means of existing models and a novel phenomenological microscopic model. This improved technique iterates between translation-rotation and rotation-vibration exchanges; equilibrium is in this way promoted if the model for the latter process is compatible with quantized oscillators. The iteration-equipartition model retains computational simplicity and promotes thermal equilibrium, even in the case of nondegenerate anharmonic quantized oscillators and multispecies gas mixtures.

Haas, Brian L.↗

Multilayer Relaxation and Surface Energies of FCC and BCC Metals Using Equivalent Crystal Theory

The multilayer relaxation of fcc and bcc metal surfaces is calculated using equivalent crystal theory. The results for changes in interplanar spacings of planes close to the surface and the ensuing surface energies are discussed in reference to other theoretical results and compared to available experimental data. The calculation includes high-index surfaces for which no other theoretical results are known.

Rodriguez, Agustin M.↗

A biharmonic relaxation method for calculating thermal stress in cooled irregular cylinders

A numerical method was developed for calculating thermal stresses in irregular cylinders cooled by one or more internal passages. The use of relaxation methods and elementary methods of finite differences was found to give approximations to the correct values when compared with previously known solutions for concentric circular cylinders possessing symmetrical and asymmetrical temperature distributions.

Holms, Arthur G↗

Thermal history effects on electrical relaxation and conductivity for potassium silicate glass with low alkali concentrations

Electrical response measurements from 10 Hz to 100 kHz between 120 and 540 C were made on potassium-silicate glasses with alkali oxide contents of 2, 3, 5 and 10 mol percent. Low alkali content glasses were chosen in order to try to reduce the Coulombic interactions between alkali ions to the point that frozen structural effects from the glass could be observed. Conductivity and electrical relaxation responses for both annealed and quenched glasses of the same composition were compared. Lower DC conductivity (sigma(sub DC)) activation energies were measured for the quenched compared to the annealed glasses. The two glasses with the lowest alkali contents exhibited a non-Arrhenius concave up curvature in the log(sigma(sub DC)) against 1/T plots, which decreased upon quenching. A sharp decrease in sigma(sub DC) was observed for glasses containing K2O concentrations of 5 mol percent or less. The log modulus loss peak (M'') maximum frequency plots against 1/T all showed Arrhenius behavior for both annealed and quenched samples. The activation energies for these plots closely agreed with the sigma(sub DC) activation energies. A sharp increase in activation energy was observed for both series as the potassium oxide concentration decreased. Changes in the electrical response are attributed to structural effects due to different alkali concentrations. Differences between the annealed and quenched response are linked to a change in the distribution of activation energies (DAE).

Angel, Paul W.↗

Optimal convolution SOR acceleration of waveform relaxation with application to semiconductor device simulation

In this paper we describe a novel generalized SOR (successive overrelaxation) algorithm for accelerating the convergence of the dynamic iteration method known as waveform relaxation. A new convolution SOR algorithm is presented, along with a theorem for determining the optimal convolution SOR parameter. Both analytic and experimental results are given to demonstrate that the convergence of the convolution SOR algorithm is substantially faster than that of the more obvious frequency-independent waveform SOR algorithm. Finally, to demonstrate the general applicability of this new method, it is used to solve the differential-algebraic system generated by spatial discretization of the time-dependent semiconductor device equations.

Reichelt, Mark↗

A note on windowing for the waveform relaxation

The technique of windowing has been often used in the implementation of the waveform relaxations for solving ODE's or time dependent PDE's. Its efficiency depends upon problem stiffness and operator splitting. Using model problems, the estimates for window length and convergence rate are derived. The electiveness of windowing is then investigated for non-stiff and stiff cases respectively. lt concludes that for the former, windowing is highly recommended when a large discrepancy exists between the convergence rate on a time interval and the ones on its subintervals. For the latter, windowing does not provide any computational advantage if machine features are disregarded. The discussion is supported by experimental results.

Zhang, Hong↗

Nonlinear structural response using adaptive dynamic relaxation on a massively-parallel-processing system

A parallel adaptive dynamic relaxation (ADR) algorithm has been developed for nonlinear structural analysis. This algorithm has minimal memory requirements, is easily parallelizable and scalable to many processors, and is generally very reliable and efficient for highly nonlinear problems. Performance evaluations on single-processor computers have shown that the ADR algorithm is reliable and highly vectorizable, and that it is competitive with direct solution methods for the highly nonlinear problems considered. The present algorithm is implemented on the 512-processor Intel Touchstone DELTA system at Caltech, and it is designed to minimize the extent and frequency of interprocessor communication. The algorithm has been used to solve for the nonlinear static response of two and three dimensional hyperelastic systems involving contact. Impressive relative speedups have been achieved and demonstrate the high scalability of the ADR algorithm. For the class of problems addressed, the ADR algorithm represents a very promising approach for parallel-vector processing.

Oakley, David R.↗

Adaptive relaxation for the steady-state analysis of Markov chains

We consider a variant of the well-known Gauss-Seidel method for the solution of Markov chains in steady state. Whereas the standard algorithm visits each state exactly once per iteration in a predetermined order, the alternative approach uses a dynamic strategy. A set of states to be visited is maintained which can grow and shrink as the computation progresses. In this manner, we hope to concentrate the computational work in those areas of the chain in which maximum improvement in the solution can be achieved. We consider the adaptive approach both as a solver in its own right and as a relaxation method within the multi-level algorithm. Experimental results show significant computational savings in both cases.

Horton, Graham↗

Modeling near wall effects in second moment closures by elliptic relaxation

The elliptic relaxation model of Durbin (1993) for modeling near-wall turbulence using second moment closures (SMC) is compared to DNS data for a channel flow at Re(sub t) = 395. The agreement for second order statistics and even the terms in their balance equation is quite satisfactory, confirming that very little viscous effects (via Kolmogoroff scales) need to be added to the high Reynolds versions of SMC for near-wall-turbulence. The essential near-wall feature is thus the kinematic blocking effect that a solid wall exerts on the turbulence through the fluctuating pressure, which is best modeled by an elliptic operator. Above the transition layer, the effect of the original elliptic operator decays rapidly, and it is suggested that the log-layer is better reproduced by adding a non-homogeneous reduction of the return to isotropy, the gradient of the turbulent length scale being used as a measure of the inhomogeneity of the log-layer. The elliptic operator was quite easily applied to the non-linear Craft & Launder pressure-strain model yielding an improved distinction between the spanwise and wall normal stresses, although at higher Reynolds number (Re) and away from the wall, the streamwise component is severely underpredicted, as well as the transition in the mean velocity from the log to the wake profiles. In this area a significant change of behavior was observed in the DNS pressure-strain term, entirely ignored in the models.

Laurence, D.↗

Multigrid convergence of an implicit symmetric relaxation scheme

The multigrid method has been applied to an existing three-dimensional compressible Euler solver to accelerate the convergence of the implicit symmetric relaxation scheme. This lower-upper symmetric Gauss-Seidel implicit scheme is shown to be an effective multigrid driver in three dimensions. A grid refinement study is performed including the effects of large cell aspect ratio meshes. Performance figures of the present multigrid code on Cray computers including the new C90 are presented. A reduction of three orders of magnitude in the residual for a three-dimensional transonic inviscid flow using 920 k grid points is obtained in less than 4 min on a Cray C90.

Yoon, Seokkwan↗

Data-parallel lower-upper relaxation method for reacting flows

The implicit lower-upper symmetric Gauss-Seidel (LU-SGS) method of Yoon and Jameson is modified for use on massively parallel computers. The method has been implemented on the Thinking Machines CM-5 and the MasPar MP-1 and MP-2, where large percentages of the theoretical peak floating point performance are obtained. It is shown that the new data-parallel LU relaxation method has better convergence properties than the original method for two different inviscid compressible flow simulations. The convergence is also improved for five-species reacting air computations. The performance of the method on various partitions of the CM-5 and on the MasPar computers is discussed. The new method shows promise for the efficient simulation of very large perfect gas and reacting flows.

Candler, Graham V.↗

Relaxation approximation in the theory of shear turbulence

Leslie's perturbative treatment of the direct interaction approximation for shear turbulence (Modern Developments in the Theory of Turbulence, 1972) is applied to derive a time dependent model for the Reynolds stresses. The stresses are decomposed into tensor components which satisfy coupled linear relaxation equations; the present theory therefore differs from phenomenological Reynolds stress closures in which the time derivatives of the stresses are expressed in terms of the stresses themselves. The theory accounts naturally for the time dependence of the Reynolds normal stress ratios in simple shear flow. The distortion of wavenumber space by the mean shear plays a crucial role in this theory.

Rubinstein, Robert↗

User's Manual for the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA)

This user's manual provides detailed instructions for the installation and the application of version 4.1 of the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA). Also provides simulation of flow field in thermochemical nonequilibrium around vehicles traveling at hypersonic velocities through the atmosphere. Earlier versions of LAURA were predominantly research codes, and they had minimal (or no) documentation. This manual describes UNIX-based utilities for customizing the code for special applications that also minimize system resource requirements. The algorithm is reviewed, and the various program options are related to specific equations and variables in the theoretical development.

Gnoffo, Peter A.↗

Metastable State Relaxation in a Gravitational Field

A metastable state relaxation equation for a physical system placed into a gravitational field is constructed for non-critical supersaturated solutions which arc in the immediate neighborhood of the coexistence line. Solutions of this equation are obtained in two different regimes: stationary and dynamic. The sedimentation time which can be defined as the time of the subcritical solute cluster redistribution corresponding to the final steady state in the gravitational field is found. The formation of the concentration gradient is proved analytically and its expression through the model parameters is obtained. The following analysis gives the expression for the sedimentation time which does not depend on the column height. The law of the concentration change with respect to the column height is also found and analyzed.

Izmailov, Alexander F.↗

Global Modeling and Data Assimilation: Documentation of the Tangent Linear and Adjoint Models of the Relaxed Arakawa-Schubert Moisture Parameterization of the NASA GEOS-1 GCM - Volume 11

A detailed description of the development of the tangent linear model (TLM) and its adjoint model of the Relaxed Arakawa-Schubert moisture parameterization package used in the NASA GEOS-1 C-Grid GCM (Version 5.2) is presented. The notational conventions used in the TLM and its adjoint codes are described in detail.

Suarez, Max J.↗

A Pseubo-Temporal Multi-Grid Relaxation Scheme for Solving the Parabolized Navier-Stokes Equations

A multi-grid, flux-difference-split, finite-volume code, VULCAN, is presented for solving the elliptic and parabolized form of the equations governing three-dimensional, turbulent, calorically perfect and non-equilibrium chemically reacting flows. The space marching algorithms developed to improve convergence rate and or reduce computational cost are emphasized. The algorithms presented are extensions to the class of implicit pseudo-time iterative, upwind space-marching schemes. A full approximate storage, full multi-grid scheme is also described which is used to accelerate the convergence of a Gauss-Seidel relaxation method. The multi-grid algorithm is shown to significantly improve convergence on high aspect ratio grids.

Morrison, J. H.↗

Design, Evaluation and GCM-Performance of a New Parameterization for Microphysics of Clouds with Relaxed Arakawa-Schubert Scheme (McRas)

A prognostic cloud scheme named McRAS (Microphysics of clouds with Relaxed Arakawa-Schubert Scheme) was developed with the aim of improving cloud-microphysics, and cloud-radiation interactions in GCMs. McRAS distinguishes convective, stratiform, and boundary-layer clouds. The convective clouds merge into stratiform clouds on an hourly time-scale, while the boundary-layer clouds do so instantly. The cloud condensate transforms into precipitation following the auto-conversion relations of Sundqvist that contain a parametric adaptation for the Bergeron-Findeisen process of ice crystal growth and collection of cloud condensate by precipitation. All clouds convect, advect, and diffuse both horizontally and vertically with a fully active cloud-microphysics throughout its life-cycle, while the optical properties of clouds are derived from the statistical distribution of hydrometeors and idealized cloud geometry. An evaluation of McRAS in a single column model (SCM) with the GATE Phase III data has shown that McRAS can simulate the observed temperature, humidity, and precipitation without discernible systematic errors. An evaluation with the ARM-CART SCM data in a cloud model intercomparison exercise shows reasonable but not an outstanding accurate simulation. Such a discrepancy is common to almost all models and is related, in part, to the input data quality. McRAS was implemented in the GEOS II GCM. A 50 month integration that was initialized with the ECMWF analysis of observations for January 1, 1987 and forced with the observed sea-surface temperatures and sea-ice distribution and vegetation properties (biomes, and soils), with prognostic soil moisture, snow-cover, and hydrology showed a very realistic simulation of cloud process, incloud water and ice, and cloud-radiative forcing (CRF). The simulated ITCZ showed a realistic time-mean structure and seasonal cycle, while the simulated CRF showed sensitivity to vertical distribution of cloud water which can be easily altered by the choice of time constant and incloud critical cloud water amount regulators for auto-conversion. The CRF and its feedbacks also have a profound effect on the ITCZ. Even though somewhat weaker than observed, the McRAS-GCM simulation produces robust 30-60 day oscillations in the 200 hPa velocity potential. Two ensembles of 4-summer (July, August, September) simulations, one each for 1987 and 1988 show that the McRAS-GCM simulates realistic and statistically significant precipitation differences over India, Central America, and tropical Africa. Several seasonal simulations were performed with McRAS-GEOS II GCM for the summer (June-July- August) and winter (December-January-February) periods to determine how the simulated clouds and CRFs would be affected by: i) advection of clouds; ii) cloud top entrainment instability, iii) cloud water inhomogeneity correction, and (iv) cloud production and dissipation in different cloud-processes. The results show that each of these processes contributes to the simulated cloud-fraction and CRF.

Sud, Y. C.↗

ASCA Temperature Maps for Merging and Relaxed Clusters and Physics of the Cluster Gas

ASCA temperature maps for several galaxy clusters undergoing strong mergers will be presented. From these maps, it is possible to estimate velocities of the colliding subclusters. I will discuss several interesting implications of these estimates for the physics of the cluster gas and the shape of the gravitational potential. I will also present temperature maps and profiles for several relaxed clusters selected for X-ray mass determination, and present the mass values derived without the assumption of isothermality. The accurate mass-temperature and luminosity-temperature relations will be discussed. This talk will review how AXAF will revolutionize X-ray astronomy through its radically better imaging and spectroscopic resolution. Examples from many fields of astrophysics will be given.

Markevitch, M.↗