GENERALIZATIONS OF THE ENERGY-FLUX PARABOLIC EQUATION

2005 ◽  
Vol 13 (04) ◽  
pp. 641-665 ◽  
Author(s):  
DMITRY MIKHIN
Keyword(s):  
Energy Conservation ◽  
Energy Flux ◽  
Parabolic Equations ◽  
Acoustic Pressure ◽  
Large Range ◽  
Accurate Solution ◽  
Small Range ◽  
Model Following ◽  
Energy Conserving ◽  
Nicolson Scheme

Parabolic equations written in terms of energy flux are inherently immune to the problem of energy conservation at vertical interfaces. Mikhin [J. Comp. Acoust. 9 (2001) 183–203] achieved exact reciprocity and energy conservation in a finite-difference PE model following this approach. However, his model used the implicit Crank–Nicolson scheme in range that requires a small range step for accurate solution. The present paper generalizes the exponential propagator of Collins [J. Acoust. Soc. Am. 93 (1993) 1736–1742] to solve the energy-flux PE. The obtained solution remains strictly reciprocal and energy conserving, while allowing large range steps. The numerical efficiency is improved by one or two orders of magnitude. A technique is proposed to calculate the acoustic pressure within the large steps, so the solution combines fast advance in range with dense range sampling. Numerical examples are provided.

scholarly journals Numerical Development and Evaluation of an Energy Conserving Conceptual Stochastic Climate Model

2019 ◽  
Vol 5 (1) ◽  
pp. 45-64 ◽  
Author(s):  
Federica Gugole ◽  
Christian L. E. Franzke
Keyword(s):  
Energy Conservation ◽  
Total Energy ◽  
Prediction Models ◽  
Climate Model ◽  
Empirical Orthogonal Functions ◽  
Correlated Noise ◽  
Spatial Covariance ◽  
Conservation Of Energy ◽  
Stochastic Climate Model ◽  
Energy Conserving

AbstractIn this study we aim to present the successful development of an energy conserving conceptual stochastic climate model based on the inviscid 2-layer Quasi-Geostrophic (QG) equations. The stochastic terms have been systematically derived and introduced in such away that the total energy is conserved. In this proof of concept studywe give particular emphasis to the numerical aspects of energy conservation in a highdimensional complex stochastic system andwe analyzewhat kind of assumptions regarding the noise should be considered in order to obtain physical meaningful results. Our results show that the stochastic model conserves energy to an accuracy of about 0.5% of the total energy; this level of accuracy is not affected by the introduction of the noise, but is mainly due to the level of accuracy of the deterministic discretization of the QG model. Furthermore, our results demonstrate that spatially correlated noise is necessary for the conservation of energy and the preservation of important statistical properties, while using spatially uncorrelated noise violates energy conservation and gives unphysical results. A dynamically consistent spatial covariance structure is determined through Empirical Orthogonal Functions (EOFs). We find that only a small number of EOFs is needed to get good results with respect to energy conservation, autocorrelation functions, PDFs and eddy length scale when comparing a deterministic control simulation on a 512 × 512 grid to a stochastic simulation on a 128 × 128 grid. Our stochastic approach has the potential to seamlessly be implemented in comprehensive weather and climate prediction models.

scholarly journals Characterizing and modeling of low twist yarn mechanics

2019 ◽  
Vol 14 ◽  
pp. 155892501986694
Author(s):  
Benjamin K O Cheung ◽  
Jason P Carey
Keyword(s):  
Linear Regression ◽  
Standard Error ◽  
Prediction Models ◽  
Large Range ◽  
Short Fiber ◽  
Regenerated Cellulose ◽  
Small Range ◽  
Longitudinal Stiffness ◽  
Simple Linear Relationship ◽  
Multifilament Yarns

Twist in yarns can be used for handling or testing purposes, but it is not necessary when using continuous multifilament yarns as compared to the spinning required for a short fiber yarn. Small amounts of twist have shown to increase the strength of the yarn while decreasing the longitudinal stiffness. Previous models, including Gegauff’s cos2 θ model and Rao and Farris’ model, are compared and discussed. A para-aramid (Kevlar 49) and a regenerated cellulose (BioMid) yarn are tested at various levels of twist to compare with these models. Twist is manually applied, and the samples are tested under continuous rate of extension to determine chord modulus, breaking tenacity, and elongation and break. The results are then fit to existing prediction models using a minimization of the standard error of the regression. Finally, a linear regression is also applied to the data to contrast the fit compared to traditional models. It was found that while the Gegauff model and the Rao and Farris model may capture the overall trend and decrease in longitudinal stiffness over a large range of twist, the small range over which twist can practically be used is not well represented by these models and is better represented by a simple linear relationship.

scholarly journals ENERGY-CONSERVING AND RECIPROCAL SOLUTIONS FOR HIGHER-ORDER PARABOLIC EQUATIONS

2001 ◽  
Vol 09 (01) ◽  
pp. 183-203 ◽  
Author(s):  
DMITRY MIKHIN
Keyword(s):  
Finite Difference ◽  
Energy Conservation ◽  
Difference Scheme ◽  
Numerical Solution ◽  
Finite Difference Scheme ◽  
Flow Reversal ◽  
Difference Operators ◽  
Energy Conserving ◽  
The One ◽  
Moving Media

The energy conservation law and the flow reversal theorem are valid for underwater acoustic fields. In media at rest the theorem transforms into well-known reciprocity principle. The presented parabolic equation (PE) model strictly preserves these important physical properties in the numerical solution. The new PE is obtained from the one-way wave equation by Godin12 via Padé approximation of the square root operator and generalized to the case of moving media. The PE is range-dependent and explicitly includes range derivatives of the medium parameters. Implicit finite difference scheme solves the PE written in terms of energy flux. Such formalism inherently provides simple and exact energy-conserving boundary condition at vertical interfaces. The finite-difference operators, the discreet boundary conditions, and the self-starter are derived by discretization of the differential PE. Discreet energy conservation and flow reversal theorem are rigorously proved as mathematical properties of the finite-difference scheme and confirmed by numerical modeling. Numerical solution is shown to be reciprocal with accuracy of 10–12 decimal digits, which is the accuracy of round-off errors. Energy conservation and wide-angle capabilities of the model are illustrated by comparison with two-way normal mode solutions including the ASA benchmark wedge.

scholarly journals Derivation of Boussinesq's shoaling law using a coupled BBM system

2013 ◽  
Vol 20 (2) ◽  
pp. 213-219 ◽  
Author(s):  
H. Kalisch ◽  
A. Senthilkumar
Keyword(s):  
Energy Density ◽  
Solitary Wave ◽  
Energy Conservation ◽  
Energy Flux ◽  
Solitary Waves ◽  
Principle Of Energy Conservation

Abstract. This paper is focused on finding rules for waveheight change in a solitary wave as it runs up a slowly increasing bottom. A coupled BBM system is used to describe the solitary waves. Expressions for energy density and energy flux associated with the BBM system are derived, and the principle of energy conservation is used to develop an equation relating the waveheight and undisturbed depth to the initial undisturbed depth and the incident waveheight. In the limit of zero waveheight, Boussinesq's shoaling law is recovered.

scholarly journals Solution of Point Reactor Neutron Kinetics Equations with Temperature Feedback by Singularly Perturbed Method

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Wenzhen Chen ◽  
Jianli Hao ◽  
Ling Chen ◽  
Haofeng Li
Keyword(s):  
Nuclear Reactor ◽  
Large Range ◽  
Accurate Solution ◽  
Average Density ◽  
Singularly Perturbed ◽  
Neutron Density ◽  
Delayed Neutron ◽  
Small Step ◽  
Neutron Kinetics ◽  
Temperature Feedback

The singularly perturbed method (SPM) is proposed to obtain the analytical solution for the delayed supercritical process of nuclear reactor with temperature feedback and small step reactivity inserted. The relation between the reactivity and time is derived. Also, the neutron density (or power) and the average density of delayed neutron precursors as the function of reactivity are presented. The variations of neutron density (or power) and temperature with time are calculated and plotted and compared with those by accurate solution and other analytical methods. It is shown that the results by the SPM are valid and accurate in the large range and the SPM is simpler than those in the previous literature.

A Mass and Energy Conserving Finite Element Lubrication Algorithm

1994 ◽  
Vol 116 (4) ◽  
pp. 667-671 ◽  
Author(s):  
A. Kumar ◽  
J. F. Booker
Keyword(s):  
Finite Element ◽  
Energy Conservation ◽  
Computational Effort ◽  
Lubricant Film ◽  
Cavitation Model ◽  
Energy Conserving

A previous mass-conserving finite element cavitation model is extended to include energy conservation in the lubricant film. The extension introduces no additional iteration and very little additional computational effort.

Sacrificing Environmental Control for Energy Conservation—A Consultant's Viewpoint

1978 ◽  
Vol 22 (1) ◽  
pp. 532-532 ◽  
Author(s):  
Richard B. Hayter
Keyword(s):  
Energy Conservation ◽  
Control Systems ◽  
Energy Management ◽  
Environmental Conditions ◽  
Environmental Control ◽  
Related Effect ◽  
Management Consultant ◽  
Energy Conserving ◽  
Energy Manager

An energy management consultant has a number of options available to him to conserve energy in existing or new building environmental control systems. Unfortunately, many of the options may also reduce the precision in maintaining a desired set of environmental conditions. Therefore, the energy manager must seek to maximize energy conserved yet minimuze occupant discomfort. A number of energy conserving environmental control modifications are described as well as the related effect they may have on the degree of occupant discomfort.

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