Total energy conservation and the symplectic algorithm

2002 ◽  
Vol 19 (3) ◽  
pp. 459-467 ◽  
Author(s):  
Ji Zhongzhen ◽  
Wang Bin ◽  
Zhao Ying ◽  
Yang Hongwei
Keyword(s):  
Energy Conservation ◽  
Total Energy ◽  
Symplectic Algorithm ◽  
Total Energy Conservation

Total energy conservation in ALE schemes for compressible flows

2010 ◽  
Vol 19 (4) ◽  
pp. 337-363 ◽  
Author(s):  
Alain Dervieux ◽  
Charbel Farhat ◽  
Bruno Koobus ◽  
Mariano Vázquez
Keyword(s):  
Energy Conservation ◽  
Total Energy ◽  
Compressible Flows ◽  
Total Energy Conservation

scholarly journals Incorporating the Work Done by Vertical Density Fluxes in Both Kinetic and Thermal Energy Conservation Equations to Satisfy Total Energy Conservation

2019 ◽  
Vol 58 (2) ◽  
pp. 213-230 ◽  
Author(s):  
Jielun Sun
Keyword(s):  
Thermal Expansion ◽  
Energy Balance ◽  
Kinetic Energy ◽  
Potential Energy ◽  
Energy Conservation ◽  
Total Energy ◽  
Thermal Energy ◽  
Temporal Variations ◽  
Vertical Density ◽  
Total Energy Conservation

AbstractConservation of total, kinetic, and thermal energy in the atmosphere is revisited, and the derived thermal energy balance is examined with observations. Total energy conservation (TEC) provides a constraint for the sum of kinetic, thermal, and potential energy changes. In response to air thermal expansion/compression, air density variation leads to vertical density fluxes and potential energy changes, which in turn impact the thermal energy balance as well as the kinetic energy balance due to the constraint of TEC. As vertical density fluxes can propagate through a large vertical domain to where local thermal expansion/compression becomes negligibly small, interactions between kinetic and thermal energy changes in determining atmospheric motions and thermodynamic structures can occur when local diabatic heating/cooling becomes small. The contribution of vertical density fluxes to the kinetic energy balance is sometimes considered but that to the thermal energy balance is traditionally missed. Misinterpretation between air thermal expansion/compression and incompressibility for air volume changes with pressure under a constant temperature would lead to overlooking important impacts of thermal expansion/compression on air motions and atmospheric thermodynamics. Atmospheric boundary layer observations qualitatively confirm the contribution of potential energy changes associated with vertical density fluxes in the thermal energy balance for explaining temporal variations of air temperature.

A new method for constructing total energy conservation algorithms*

2003 ◽  
Vol 13 (1) ◽  
pp. 59-62
Author(s):  
Ying Zhao ◽  
Zhongzhen Ji ◽  
Hongwei Yang ◽  
Bin Wang
Keyword(s):  
Energy Conservation ◽  
Total Energy ◽  
New Method ◽  
Total Energy Conservation

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.

A Theoretical Study on Decentralized Space Heating System

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Zhi-Ping Song
Keyword(s):  
Energy Conservation ◽  
Total Energy ◽  
Global Climate ◽  
Energy System ◽  
Specific Consumption ◽  
Space Heating ◽  
Full Potential ◽  
Heating Systems ◽  
End Use ◽  
The Impact

Global climate change mitigation requires the fossil fuel consumption substantially reduced. Space heating is an energy-consuming sector. Despite the fact that the thermal efficiency of current space heating systems has achieved a value higher than 85%, corresponding to lower than 40kg c.e./GJ, there is still a big potential for energy conservation. In order to realize the full potential, investigations of heating systems should appeal to reversibility/exergy analysis made on total energy concept basis. This paper starts with an introduction of the concept “reversible mode of heating,” leading the readers think of space heating in terms of reversibility. Right after, a systematic reversibility analysis on a “mine to home” basis is conducted to reveal the impact of any irreversibility of all subsystems or devices involved in the total energy system of heating on the fuel/monetary specific consumption of unit end-use heat. The paper points out that although combined heat and power (CHP) and electrically driven heat pump are both of “reversible mode,” the former is far more favorable in terms of energy conservation. The recently ascent decentralized energy system provides the best circumstances for CHP implementation. The demand-side improvement is a topic of most importance but frequently neglected. This study reveals that, if properly engineered, this improvement together with adopting a direct type of heat grid might lower the fuel specific consumption of end-use heat of CHP to a level as low as 13–9kg c.e./GJ.

scholarly journals Inherent dissipation of upwind-biased potential temperature advection and its feedback on model dynamics

2021 ◽  
Author(s):  
Almut Gaßmann
Keyword(s):  
Energy Conservation ◽  
Pressure Gradient ◽  
Potential Temperature ◽  
Gradient Term ◽  
Advection Scheme ◽  
Temperature Advection ◽  
Advection Schemes ◽  
Pressure Gradient Term ◽  
Diffusive Fluxes ◽  
Total Energy Conservation

<p>Higher order upwind biased advection schemes are often used for potential temperature advection in dynamical cores of atmospheric models. The inherent diffusive and anti-diffusive fluxes are interpreted here as the effect of irreversible sub-gridscale dynamics. For those, total energy conservation and positive internal entropy production must be guaranteed. As a consequence of energy conservation, the pressure gradient term should be formulated in Exner pressure form. The presence of local antidiffusive fluxes in potential temperature advection schemes foils the validity of the second law of thermodynamics. Due to this failure, a spurious wind acceleration into the wrong direction is locally induced via the pressure gradient term. When correcting the advection scheme to be more entropically consistent, the spurious acceleration is avoided, but two side effects come to the fore: (i) the overall accuracy of the advection scheme decreases and (ii) the now purely diffusive fluxes become more discontinuous compared to the original ones, which leads to more sudden body forces in the momentum equation. Therefore the amplitudes of excited gravity waves from jets and fronts increase compared to the original formulation with inherent local antidiffusive fluxes.</p><p>The means used for supporting the argumentation line are theoretical arguments concerning total energy conservation and internal entropy production, pure advection tests, one-dimensional advection-dynamics interaction tests and evaluation of runs with a global atmospheric dry dynamical core.</p>

scholarly journals On Fulfillment of Energy Conservation Law in Theory of Elastic Waves V. V. Nevdakh1)

2021 ◽  
Vol 20 (2) ◽  
pp. 161-167
Author(s):  
V. V. Nevdakh
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Energy Conservation ◽  
Elastic Wave ◽  
Total Energy ◽  
Elastic Deformation ◽  
Sound Wave ◽  
Elastic Waves ◽  
Conservation Law ◽  
Energy Conservation Law

In accordance with the energy conservation law, the total energy of a closed physical system must remain constant at any moment of time. The energy of a traveling elastic wave consists of the kinetic energy in the oscillating particles of the medium and the potential energy of  its elastic deformation. In the existing theory of elastic waves, it is believed that the kinetic and potential energy densities of a traveling wave without losses  are the same at any moment of time and vary according to the same law. Accordingly, the total energy density of such wave is different at various moment of time, and only its time-averaged value remains constant. Thus, in the existing theory of elastic waves, the energy conservation law is not fulfilled. The purpose of this work is to give a physically correct description of these waves. A new description of a sound wave in an ideal gas has been proposed and it is based on the use of a wave equation system for perturbing the oscillation velocity of gas particles, which determines their kinetic energy, and for elastic deformation, which determines their potential energy. It has been shown that harmonic solutions describing the oscillations of the gas particles velocity perturbation and their elastic deformation, which are phase shifted by p/2, are considered as physically correct solutions of such equations system for a traveling sound wave. It has been found that the positions of the kinetic and potential energy maxima in the elastic wave, described by such solutions, alternate in space every quarter of the wavelength. It has been established that every quarter of a period in a wave without losses, the kinetic energy is completely converted to potential and vice versa, while at each spatial point of the wave its total energy density is the same at any time, which is consistent with the energy conservation law. The energy flux density of such traveling elastic wave is described by the expression for the Umov vector. It has been concluded that such traveling sound wave without losses  in an ideal gas can be considered as a harmonic oscillator.

Energy Flow Analysis and Energy Conservation and Emission Reduction in Sichuan Province, China

2014 ◽  
Vol 521 ◽  
pp. 819-824
Author(s):  
Wei Liu ◽  
Xi Yu Feng ◽  
Guan Huang ◽  
Han Qing Huan
Keyword(s):  
Growth Rate ◽  
Energy Consumption ◽  
Energy Conservation ◽  
Total Energy ◽  
Emission Reduction ◽  
Sichuan Province ◽  
Average Annual Growth Rate ◽  
Annual Growth Rate ◽  
Total Energy Consumption ◽  
Pollutants Emission

Based on the relative data and materials, the energy flowchart of Sichuan province in 2008 was drew at first, then the energy input, output, consumption, corresponding pollutants emission of Sichuan province from 2000 to 2008 were analysed simultaneously. The results show that the total energy consumption reaches up to about 15144.96 tons of standard coal in 2008, the average annual growth rate is 8.42%. Coal and non-fossil energy consumption accounts for 65.35% and 8.44% of total energy consumption respectively. SO2 emissions decreases by an average annual rate of 4.03% since 2005, but NOX and CO2 emissions increases with average annual growth rate of 6.58% and 8.37% respectively. In addition, the energy consumption and pollutants emission of Sichuan province during "the 12th Five-Year Plan" are predicted and analysed within different scenario, then the development plan is proposed. Finally, suggestions of energy conservation and emission reduction in Sichuan province are proposed.

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