Non-uniqueness of signed measure-valued solutions to the continuity equation in presence of a unique flow

The numerical simulation of flow process and heat transfer phenomena demands the solution of continuous differential equation and energy-conservation equations coupled with the continuity equation. The choosing of computation parameters in numerical simulation of computation domain have influence on accuracy of obtained results. The choose parameters, as mesh density, mesh type and computation procedures, for the numerical diffusion of computation domain were analysed and compared. The CFD simulation in ANSYS – Fluent was used for numerical simulation of 3D stational temperature flow of the computation domain.

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Nonstationary Superconductivity: Quantum Dissipation and Time-Dependent Ginzburg-Landau Equation

Advances in Condensed Matter Physics ◽

10.1155/2011/425328 ◽

2011 ◽

Vol 2011 ◽

pp. 1-10

Author(s):

Anatoly A. Barybin

Keyword(s):

Order Parameter ◽

Continuity Equation ◽

Chemical Potential ◽

Landau Equation ◽

Time Dependent ◽

Quantum Dissipation ◽

Ginzburg Landau ◽

Superfluid Component ◽

Ginzburg Landau Equation ◽

Conservation Property

Transport equations of the macroscopic superfluid dynamics are revised on the basis of a combination of the conventional (stationary) Ginzburg-Landau equation and Schrödinger's equation for the macroscopic wave function (often called the order parameter) by using the well-known Madelung-Feynman approach to representation of the quantum-mechanical equations in hydrodynamic form. Such an approach has given (a) three different contributions to the resulting chemical potential for the superfluid component, (b) a general hydrodynamic equation of superfluid motion, (c) the continuity equation for superfluid flow with a relaxation term involving the phenomenological parameters and , (d) a new version of the time-dependent Ginzburg-Landau equation for the modulus of the order parameter which takes into account dissipation effects and reflects the charge conservation property for the superfluid component. The conventional Ginzburg-Landau equation also follows from our continuity equation as a particular case of stationarity. All the results obtained are mutually consistent within the scope of the chosen phenomenological description and, being model-neutral, applicable to both the low- and high- superconductors.

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Multiple Vortex Body Vortex Numerical Simulation

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.328-330.1755 ◽

2011 ◽

Vol 328-330 ◽

pp. 1755-1758

Author(s):

Han Xiao Liu ◽

Zhong Liu ◽

Huai Liang Li ◽

Xin Xin Feng ◽

Zhen Zhong Xing

Keyword(s):

Numerical Simulation ◽

Flow Field ◽

Turbulence Intensity ◽

Continuity Equation ◽

Momentum Equation ◽

Turbulent Intensity ◽

Good Effect ◽

Train Of Thought

In this paper, the continuity equation, momentum equation and the k-ε turbulence equation were introduced to simulate the flow field of the multiple vortex bodies in different spacing cases. Found that each vortex body had good effect in producing vortex, and the greater flow field spacing, the smaller the highest velocity; the turbulence intensity is increasing gradually from the former vortex body to the next one, and there may be a best spacing between the vortex bodies which makes the best turbulent intensity. All of these theories provide a train of thought for the turbulent coalescence mechanism.

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