On a momentum interpolation scheme for collocated meshes with improved discrete kinetic energy conservation

2019 ◽  
Vol 33 (6) ◽  
pp. 2761-2768
Author(s):  
Wook Lee ◽  
Eunbeom Jung ◽  
Seongwon Kang ◽  
Nahmkeon Hur
Keyword(s):  
Kinetic Energy ◽  
Energy Conservation ◽  
Interpolation Scheme

scholarly journals Impact of difference between explicit and implicit second-order time integration schemes on isotropic/anisotropic steady incompressible turbulence field

2021 ◽  
Vol 2090 (1) ◽  
pp. 012145
Author(s):  
Ryuma Honda ◽  
Hiroki Suzuki ◽  
Shinsuke Mochizuki
Keyword(s):  
Kinetic Energy ◽  
Energy Conservation ◽  
Integration Method ◽  
Time Integration ◽  
Second Order ◽  
Implicit Time ◽  
Explicit Time Integration ◽  
Time Integration Method ◽  
Implicit Time Integration ◽  
Time Integration Methods

Abstract This study presents the impact of the difference between the implicit and explicit time integration methods on a steady turbulent flow field. In contrast to the explicit time integration method, the implicit time integration method may produce significant kinetic energy conservation error because the widely used spatial difference method for discretizing the governing equations is explicit with respect to time. In this study, the second-order Crank-Nicolson method is used as the implicit time integration method, and the fourth-order Runge-Kutta, second-order Runge-Kutta and second-order Adams-Bashforth methods are used as explicit time integration methods. In the present study, both isotropic and anisotropic steady turbulent fields are analyzed with two values of the Reynolds number. The turbulent kinetic energy in the steady turbulent field is hardly affected by the kinetic energy conservation error. The rms values of static pressure fluctuation are significantly sensitive to the kinetic energy conservation error. These results are examined by varying the time increment value. These results are also discussed by visualizing the large scale turbulent vortex structure.

scholarly journals GRAVITY HEATS THE UNIVERSE

2009 ◽  
Vol 18 (14) ◽  
pp. 2201-2207
Author(s):  
ADAM MOSS ◽  
DOUGLAS SCOTT
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Energy Conservation ◽  
Cosmic Microwave Background ◽  
Initial Conditions ◽  
Gravitational Instability ◽  
Simplified Model ◽  
Microwave Background ◽  
Average Temperature ◽  
The Universe

Structures in the Universe grew through gravitational instability from very smooth initial conditions. Energy conservation requires that the growing negative potential energy of these structures be balanced by an increase in kinetic energy. A fraction of this is converted into heat in the collisional gas of the intergalactic medium. Using a toy model of gravitational heating, we attempt to link the growth of structure in the Universe with the average temperature of this gas. We find that the gas is rapidly heated from collapsing structures at around z ~ 10, reaching a temperature > 106 K today, depending on some assumptions of our simplified model. Before that there was a cold era from z ~ 100 to ~10 in which the matter temperature was below that of the cosmic microwave background.

Simulation of astrophysical flows in isentropic approximation

2018 ◽  
Vol 27 (10) ◽  
pp. 1844014
Author(s):  
S. G. Moiseenko ◽  
G. S. Bisnovatyi-Kogan
Keyword(s):  
Shock Wave ◽  
Kinetic Energy ◽  
Energy Conservation ◽  
Conservation Equation ◽  
Numerical Errors ◽  
Energy Conservation Equation ◽  
Different Types ◽  
Entropy Conservation ◽  
Isentropic Approximation ◽  
Astrophysical Flows

One of the difficulties of numerical simulations of cold supersonic astrophysical flows is a big difference in different types of energy. Gravitational and/or kinetic energy of the gas could be much larger than its internal energy. In such a case, it is possible to get large numerical errors in the simulations. To avoid this difficulty, conservation of entropy equation was used instead of energy conservation equation. The entropy conservation equation does not contain the gravitational and kinetic energy. The application of the isentropic set of equations is correct when the flow does not contain shocks or the amplitude of the shocks (shock wave Mach number) is not large. We estimate the violation of the energy conservation low when the “shock wave” is isentropic.

Global kinetic energy conservation with unstructured meshes

2002 ◽  
Vol 40 (3-4) ◽  
pp. 561-571 ◽  
Author(s):  
S. Benhamadouche ◽  
D. Laurence
Keyword(s):  
Kinetic Energy ◽  
Energy Conservation ◽  
Unstructured Meshes

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.

scholarly journals Modeling of Energy Release at the Final Stage of the Meteoroid Movement

2016 ◽  
Vol 27 (1) ◽  
pp. 290-293
Author(s):  
Lidia A. Egorova ◽  
Valery V. Lokhin
Keyword(s):  
High Temperature ◽  
Kinetic Energy ◽  
Energy Conservation ◽  
Thermal Energy ◽  
Final Stage ◽  
Physical Theory ◽  
Cosmic Body ◽  
Gas Volume ◽  
Gas Cloud ◽  
Explosive Destruction

Abstract The paper continues to build upon the author’s previous research on fireballs fragmentation. A model of the sudden explosive destruction of the cosmic body at the height of the maximum flash is used. After the fragmentation, the kinetic energy of the moving particles of a meteoroid passes into the thermal energy of the gas volume inwhich their motion takes place. The temperature of a gas cloud calculated analytically using energy conservation lawand equations of physical theory of meteors. The mass distribution of fragments was taken from the literature. The high temperature of the gas in a cloud allows us to talk about the phenomenon of a "thermal explosion".

Inverting DAS data using energy conservation principles

2021 ◽  
pp. 1-32 ◽  
Author(s):  
Vladimir Kazei ◽  
Konstantin Osypov
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Energy Conservation ◽  
Energy Balancing ◽  
Seismic Profiling ◽  
Vertical Seismic Profiling ◽  
Conservation Principles ◽  
Distributed Acoustic Sensing ◽  
To Come ◽  
Seismic Wavefield

Distributed acoustic sensing (DAS) technologies are now becoming widespread, in particular in Vertical Seismic Profiling (VSP). Being a spatially densely sampled recording of seismic wavefield, DAS data provides an extended measurement as compared with point geophone VSP. We developed a basic theory that enables intuitive geophysical understanding of DAS data using the concepts of kinetic and potential energy and their fluxes. We start by relating DAS and geophone measurements to potential energy and kinetic energy, correspondingly. We use this relationship and energy balancing along the well to come up with a scheme for inverting DAS and geophone wavefields for density and velocity simultaneously. Then, recognizing that it may be impractical to have both geophones and DAS, we propose a second inversion scheme that eliminates the need for geophones and uses upgoing and downgoing DAS wavefields instead. There is no need for first-break picking windowing the data and full DAS records can be utilized in both inversion schemes. We test the feasibility of these inversion schemes on 2D elastic synthetics.

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