An attempt to simulate more precisely the behavior of a solid body using new energy conservation equation for fully coupled thermal structural analysis

2008 ◽  
pp. 88-88 ◽  
Author(s):  
L. Écsi ◽  
P. Élesztös
Keyword(s):  
Structural Analysis ◽  
Energy Conservation ◽  
Solid Body ◽  
Conservation Equation ◽  
Energy Conservation Equation ◽  
New Energy ◽  
Fully Coupled

Energy conservation, time-reversal invariance and reciprocity in ducts with flow

2001 ◽  
Vol 431 ◽  
pp. 223-237 ◽  
Author(s):  
WILLI MÖHRING
Keyword(s):  
Energy Conservation ◽  
Sound Wave ◽  
Conservation Equation ◽  
Smooth Transition ◽  
Rotational Flow ◽  
Flow Energy ◽  
Energy Conservation Equation ◽  
Reversal Invariance ◽  
Edge Conditions ◽  
Piecewise Continuous

A sound wave propagating in an inhomogeneous duct consisting of two semi-infinite uniform ducts with a smooth transition region in between and which carries a steady flow is considered. The duct walls may be rigid or compliant. For an irrotational sound wave it is shown that the three properties of the title are closely related, such that the validity of any two implies the validity of the third. Furthermore it is shown that the three properties are fulfilled for lossless locally reacting duct walls provided the impedance varies at most continuously. For piecewise-continuous wall properties edge conditions are essential. By an analytic continuation argument it is shown that reciprocity remains true for walls with loss. For rotational flow, energy conservation theorems have been derived only with the help of additional potential-like variables. The inter-relation between the three properties remains valid if one considers these additional variables to be known. If only the basic gasdynamic variables in both half-ducts are known, one cannot formulate an energy conservation equation; however, reciprocity is fulfilled.

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.

Dispersion and energy conservation relations of surface waves in semi-infinite plasma

1981 ◽  
Vol 25 (2) ◽  
pp. 285-307 ◽  
Author(s):  
V. Atanssov
Keyword(s):  
Surface Wave ◽  
Energy Conservation ◽  
Surface Waves ◽  
Low Frequency ◽  
Conservation Equation ◽  
Hydrodynamic Theory ◽  
Energy Conservation Equation ◽  
Surface Wave Propagation ◽  
Electric And Magnetic Fields ◽  
Bulk Waves

The hydrodynamic theory of surface wave propagation in semi-infinite homogeneous isotropic plasma is considered. Explicit linear surface wave solutions are given for the electric and magnetic fields, charge and current densities. These solutions are used to obtain the well-known dispersion relations and, together with the general energy conservation equation, to find appropriate definitions for the energy and the energy flow densities of surface waves. These densities are associated with the dispersion relation and the group velocity by formulae similar to those for bulk waves in infinite plasmas. Both cases of high-frequency (HF) and low-frequency (LF) surface waves are considered.

A Robust Three-Phase Isenthalpic Flash Algorithm Based on Free-Water Assumption

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Ruixue Li ◽  
Huazhou Andy Li
Keyword(s):  
Energy Conservation ◽  
Oil Recovery ◽  
Pure Water ◽  
Free Water ◽  
Conservation Equation ◽  
Feasible Region ◽  
Feed Mixture ◽  
Two Phase ◽  
Energy Conservation Equation ◽  
Three Phase

Isenthalpic flash is a type of flash calculation conducted at a given pressure and enthalpy for a feed mixture. Multiphase isenthalpic flash calculations are often required in compositional simulations of steam-based enhanced oil recovery methods. Based on a free-water assumption that the aqueous phase is pure water, a robust and efficient algorithm is developed to perform isenthalpic three-phase flashes. Assuming that the feed is stable, we first determine the temperature by solving the energy conservation equation. Then, the stability test on the feed mixture is conducted at the calculated temperature and the given pressure. If the mixture is found unstable, two-phase and three-phase vapor–liquid–aqueous isenthalpic flash can be simultaneously initiated without resorting to stability tests. The outer loop is used to update the temperature by solving the energy conservation equation. The inner loop determines the phase fractions and compositions through a three-phase free-water isothermal flash. A two-phase isothermal flash will be initiated if an open feasible region in the phase fractions appears in any iteration during the three-phase flash or any of the ultimately calculated phase fractions from the three-phase flash do not belong to [0,1]. A number of example calculations for water/hydrocarbon mixtures are carried out, demonstrating that the proposed algorithm is accurate, efficient, and robust.

scholarly journals An Energy Conservation Algorithm for Nonlinear Dynamic Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Jian Pang ◽  
Yu Du ◽  
Ping Hu ◽  
Weidong Li ◽  
Z. D. Ma
Keyword(s):  
Energy Conservation ◽  
Nonlinear Problems ◽  
Current Method ◽  
Conservation Equation ◽  
Iteration Formula ◽  
Energy Conservation Equation ◽  
Numerical Result ◽  
Nonlinear Dynamic Equation ◽  
Runge Kutta Method ◽  
Runge Kutta

An energy conservation algorithm for numerically solving nonlinear multidegree-of-freedom (MDOF) dynamic equations is proposed. Firstly, by Taylor expansion and Duhamel integration, an integral iteration formula for numerically solving the nonlinear problems can be achieved. However, this formula still includes a parameter that is to be determined. Secondly, through some mathematical manipulations, the original dynamical equation can be further converted into an energy conservation equation which can then be used to determine the unknown parameter. Finally, an accurate numerical result for the nonlinear problem is achieved by substituting this parameter into the integral iteration formula. Several examples are used to compare the current method with the well-known Runge-Kutta method. They all show that the energy conservation algorithm introduced in this study can eliminate algorithm damping inherent in the Runge-Kutta algorithm and also has better stability for large integral steps.

The quasi-geostrophic theory of the thermal shallow water equations

2013 ◽  
Vol 723 ◽  
pp. 374-403 ◽  
Author(s):  
Emma S. Warneford ◽  
Paul J. Dellar
Keyword(s):  
Energy Conservation ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Fluid Layer ◽  
Conservation Equation ◽  
Rossby Number ◽  
Layer System ◽  
Energy Conservation Equation ◽  
Balanced Model ◽  
Horizontal Variations

AbstractThe thermal shallow water equations provide a depth-averaged description of motions in a fluid layer that permits horizontal variations in material properties. They typically arise through an equivalent barotropic approximation of a two-layer system, with a spatially varying density contrast due to an evolving temperature field in the active layer. We formalize a previous derivation of the quasi-geostrophic (QG) theory of these equations, by performing a direct asymptotic expansion for small Rossby number. We then present a second derivation as the small Rossby number limit of a balanced model that projects out high-frequency dynamics due to inertia-gravity waves. This latter derivation has wider validity, not being restricted to mid-latitude $\beta $-planes. We also derive their local energy conservation equation from the QG limit of a thermal shallow water pseudo-energy conservation equation. This derivation involves the ageostrophic correction to the leading-order geostrophic velocity that is eliminated in the usual derivation of a closed evolution equation for the QG potential vorticity. Finally, we derive the non-canonical Hamiltonian structure of the thermal QG equations from a decomposition in Rossby number of a pseudo-energy and Poisson bracket for the thermal shallow water equations.

scholarly journals CHANGES IN CURRENT PROPERTIES DUE TO WAVE SUPERIMPOSING

1986 ◽  
Vol 1 (20) ◽  
pp. 70 ◽  
Author(s):  
Toshiyuki Asano ◽  
Masahiro Nakagawa ◽  
Yuichi Iwagaki
Keyword(s):  
Shear Stress ◽  
Velocity Profile ◽  
Energy Conservation ◽  
Current Velocity ◽  
Conservation Equation ◽  
Bottom Shear Stress ◽  
Energy Conservation Equation ◽  
Friction Term ◽  
Mean Water Level ◽  
The Mean

Changes in current properties due to wave superimposing are investigated experimentally. Variations of the mean water level gradient and the current velocity profile after wave superimposing are examined. Experimental results are discussed in relation to the energy conservation equation including the bottom friction term. It is found that changes in current properties can be well explained by increase in the time averaged bottom shear stress.

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