Conservation laws for plane steady potential barotropic flow

2013 ◽  
Vol 24 (6) ◽  
pp. 789-801 ◽  
Author(s):  
YU. A. CHIRKUNOV ◽  
S. B. MEDVEDEV
Keyword(s):  
Conservation Laws ◽  
Velocity Potential ◽  
Zero Order ◽  
System Of Equations ◽  
Nonlinear System Of Equations ◽  
Nonlinear Conservation Laws ◽  
First Order ◽  
Barotropic Flow ◽  
Chaplygin System ◽  
Steady Potential

It is shown that the set of conservation laws for the nonlinear system of equations describing plane steady potential barotropic flow of gas is given by the set of conservation laws for the linear Chaplygin system. All the conservation laws of zero order for the Chaplygin system are found. These include both known and new nonlinear conservation laws. It is found that the number of conservation laws of the first order is not more than three, assuming that the laws do not depend on the velocity potential and are not non-obvious ones. The components of these conservation laws are quadratic with respect to the stream function and its derivatives. All the Chaplygin functions are found, for which the Chaplygin system has three non-obvious conservation laws of the first order that are independent of velocity potential. All such non-obvious first-order conservation laws are found.

On conservation laws for a viscous fluid

2017 ◽  
Vol 12 (1) ◽  
pp. 40-43
Author(s):  
S.V. Khabirov
Keyword(s):  
Viscous Fluid ◽  
Conservation Laws ◽  
Lie Algebra ◽  
Conservation Law ◽  
Equation Of Motion ◽  
Zero Order ◽  
First Order ◽  
Canonical Operator ◽  
Divergence Type

The equation of motion of viscous fluid have the divergence type of the conservation laws and admit the infinite Lie algebra of point symmetries. Canonical operators of the algebra give rise to conservation laws of the first order. This was tested for the basic operators of admitted algebra. Any conservation law may be turned by doing some canonical operator on the nontrivial conservation law. The canonical operators of the zero order of conservation laws were calculated. The problem about the calculation of canonical operators of the first order of conservation laws are supplied.

A WELL-BALANCED SCHEME USING NON-CONSERVATIVE PRODUCTS DESIGNED FOR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS WITH SOURCE TERMS

2001 ◽  
Vol 11 (02) ◽  
pp. 339-365 ◽  
Author(s):  
LAURENT GOSSE
Keyword(s):  
Asymptotic Behavior ◽  
Conservation Laws ◽  
Euler Equations ◽  
Hyperbolic Systems ◽  
Zero Order ◽  
Inhomogeneous System ◽  
Source Terms ◽  
First Order ◽  
Systems Of Conservation Laws ◽  
The Right

The aim of this paper is to present a new kind of numerical processing for hyperbolic systems of conservation laws with source terms. This is achieved by means of a non-conservative reformulation of the zero-order terms of the right-hand side of the equations. In this context, we decided to use the results of Dal Maso, Le Floch and Murat about non-conservative products, and the generalized Roe matrices introduced by Toumi to derive a first-order linearized well-balanced scheme in the sense of Greenberg and Le Roux. As a main feature, this approach is able to preserve the right asymptotic behavior of the original inhomogeneous system, which is not an obvious property. Numerical results for the Euler equations are shown to handle correctly these equilibria in various situations.

Kinetics of catalytic reduction of nitrogen oxide by carbon monoxide on CuO/Al2O3 catalyst

1983 ◽  
Vol 48 (11) ◽  
pp. 3202-3208 ◽  
Author(s):  
Zdeněk Musil ◽  
Vladimír Pour
Keyword(s):  
Carbon Monoxide ◽  
Nitrogen Oxide ◽  
Rate Equation ◽  
Catalytic Reduction ◽  
Zero Order ◽  
Spectroscopic Measurements ◽  
First Order ◽  
Ir Spectroscopic ◽  
Kinetics Of ◽  
Al2o3 Catalyst

The kinetics of the reduction of nitrogen oxide by carbon monoxide on CuO/Al2O3 catalyst (8.36 mass % CuO) were determined at temperatures between 413 and 473 K. The reaction was found to be first order in NO and zero order in CO. The observed kinetics are consistent with a rate equation derived from a mechanism proposed on the basis of IR spectroscopic measurements.

scholarly journals Nonlinear conservation laws for the Schrödinger boundary value problems of second order

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ming Ren ◽  
Shiwei Yun ◽  
Zhenping Li
Keyword(s):  
Cauchy Problem ◽  
Conservation Laws ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Maximum Modulus ◽  
Second Order ◽  
Nonlinear Conservation Laws ◽  
The Cauchy Problem ◽  
Modulus Method ◽  
Semilinear Schrödinger Equation

AbstractIn this paper, we apply a reliable combination of maximum modulus method with respect to the Schrödinger operator and Phragmén–Lindelöf method to investigate nonlinear conservation laws for the Schrödinger boundary value problems of second order. As an application, we prove the global existence to the solution for the Cauchy problem of the semilinear Schrödinger equation. The results reveal that this method is effective and simple.

Area-based speciation kinetic analysis of the multipollutant removal in Constructed Wetlands to enhance its treatment efficiency

2021 ◽  
Author(s):  
Manoj Kumar ◽  
Rajesh Singh
Keyword(s):  
Wastewater Treatment ◽  
Kinetic Analysis ◽  
Constructed Wetlands ◽  
Municipal Wastewater ◽  
Zero Order ◽  
Pollutant Removal ◽  
Municipal Wastewater Treatment ◽  
Treatment Efficiency ◽  
First Order ◽  
Present Study Area

In the present study area-based, pollutant removal kinetic analysis was considered using the Zero-order, first-order decay and efficiency loss (EL) models in the constructed wetlands (CWs) for municipal wastewater treatment....

scholarly journals Shallow water waves in a rotating rectangular basin

2000 ◽  
Vol 24 (10) ◽  
pp. 649-661 ◽  
Author(s):  
Mohamed Atef Helal
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Equations Of Motion ◽  
System Of Nonlinear Equations ◽  
System Of Equations ◽  
Order Of Approximation ◽  
Shallow Water Waves ◽  
Nonlinear System Of Equations ◽  
Rectangular Basin ◽  
Shallow Water Approximation

This paper is mainly concerned with the motion of an incompressible fluid in a slowly rotating rectangular basin. The equations of motion of such a problem with its boundary conditions are reduced to a system of nonlinear equations, which is to be solved by applying the shallow water approximation theory. Each unknown of the problem is expanded asymptotically in terms of the small parameterϵwhich generally depends on some intrinsic quantities of the problem of study. For each order of approximation, the nonlinear system of equations is presented successively. It is worthy to note that such a study has useful applications in the oceanography.

First‐order equivalent Lagrangians and conservation laws

1984 ◽  
Vol 25 (6) ◽  
pp. 1776-1779 ◽  
Author(s):  
Sergio Hojman ◽  
Javier Gómez
Keyword(s):  
Conservation Laws ◽  
First Order

A Full-System Approach of the Elastohydrodynamic Line/Point Contact Problem

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
W. Habchi ◽  
D. Eyheramendy ◽  
P. Vergne ◽  
G. Morales-Espejel
Keyword(s):  
Finite Element ◽  
Nonlinear System ◽  
System Approach ◽  
Jacobian Matrix ◽  
Point Contact ◽  
System Of Equations ◽  
Nonlinear System Of Equations ◽  
Full System ◽  
Element Discretization ◽  
Fully Coupled

The solution of the elastohydrodynamic lubrication (EHL) problem involves the simultaneous resolution of the hydrodynamic (Reynolds equation) and elastic problems (elastic deformation of the contacting surfaces). Up to now, most of the numerical works dealing with the modeling of the isothermal EHL problem were based on a weak coupling resolution of the Reynolds and elasticity equations (semi-system approach). The latter were solved separately using iterative schemes and a finite difference discretization. Very few authors attempted to solve the problem in a fully coupled way, thus solving both equations simultaneously (full-system approach). These attempts suffered from a major drawback which is the almost full Jacobian matrix of the nonlinear system of equations. This work presents a new approach for solving the fully coupled isothermal elastohydrodynamic problem using a finite element discretization of the corresponding equations. The use of the finite element method allows the use of variable unstructured meshing and different types of elements within the same model which leads to a reduced size of the problem. The nonlinear system of equations is solved using a Newton procedure which provides faster convergence rates. Suitable stabilization techniques are used to extend the solution to the case of highly loaded contacts. The complexity is the same as for classical algorithms, but an improved convergence rate, a reduced size of the problem and a sparse Jacobian matrix are obtained. Thus, the computational effort, time and memory usage are considerably reduced.

Supercritical Fluid Deposition of Ruthenium Thin Films: A Kinetic Study

2007 ◽  
Vol 992 ◽  
Author(s):  
Christos F. Karanikas ◽  
James J. Watkins
Keyword(s):  
Thin Films ◽  
Growth Rate ◽  
Deposition Temperature ◽  
Zero Order ◽  
Measurable Effect ◽  
Deposition Rates ◽  
Reaction Pressure ◽  
Deposition Kinetics ◽  
First Order ◽  
Kinetics Of

AbstractThe kinetics of the deposition of ruthenium thin films from the hydrogen assisted reduction of bis(2,2,6,6-tetramethyl-3,5-heptanedionato)(1,5-cyclooctadiene)ruthenium(II), [Ru(tmhd)2cod], in supercritical carbon dioxide was studied in order to develop a rate expression for the growth rate as well as to determine a mechanism for the process. The deposition temperature was varied from 240°C to 280°C and the apparent activation energy was 45.3 kJ/mol. Deposition rates up to 30 nm/min were attained. The deposition rate dependence on precursor concentrations between 0 and 0.2 wt. % was studied at 260°C with excess hydrogen and revealed first order deposition kinetics with respect to precursor at concentrations lower then 0.06 wt. % and zero order dependence at concentrations above 0.06 wt. %. The effect of reaction pressure on the growth rate was studied at a constant reaction temperature of 260°C and pressures between 159 bar to 200 bar and found to have no measurable effect on the growth rate.

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