Finite Differences Scheme for the Euler System of Equations in a Class of Discontinuous Functions

2005 ◽  
pp. 471-477
Author(s):  
Mahir Rasulov ◽  
Turhan Karaguler
Keyword(s):  
Finite Differences ◽  
Euler System ◽  
System Of Equations ◽  
Discontinuous Functions

scholarly journals Evaluation of the Accident Rate of a Plant Equipped with an Aging Single Protective Channel by the Method of Supplementary Variables

2021 ◽  
Vol 22 (4) ◽  
pp. 533-543
Author(s):  
L. G. Oliveira ◽  
D. G. Teixeira ◽  
P. F. Frutuoso e Melo
Keyword(s):  
Finite Differences ◽  
System Of Equations ◽  
Accident Rate ◽  
Industrial Facilities ◽  
Failure Times ◽  
Supplementary Variables ◽  
Protective System ◽  
Integral Differential Equations ◽  
Ordinary Integral ◽  
Protective Systems

This work calculates the reliability of protective systems of industrial facilities, such as nuclear, to analyze the case of equipment subject to aging, important in the extension of the qualified life of the facilities. By means of the method of supplementary variables, a system of partial and ordinary integral-differential equations was developed for the probabilities of a protective system of an aging channel. The system of equations was solved by finite differences. The method was validated by comparison with channel results with exponential failure times. The method of supplementary variables exhibits reasonable results for values of reliability attributes typical of industrial facilities.

On the Calculus of Finite Differences, and its Application to Problems in the Doctrine of Compound Interest and Certain Annuities (Continued from p. 340, vol. vii.)

1858 ◽  
Vol 8 (1) ◽  
pp. 19-24
Author(s):  
William Curtis Otter
Keyword(s):  
Finite Differences ◽  
Mathematical Theory ◽  
Discontinuous Functions ◽  
The Subject ◽  
Compound Interest

The idea of periodic or discontinuous functions was primitively introduced by Euler, and has since been the subject of extended investigation by M. Fourier, who has made some new and important applications of it in. his mathematical theory of heat.

Conical shock wave for non-isentropic compressible Euler system of equations

2016 ◽  
Vol 13 (02) ◽  
pp. 215-231 ◽  
Author(s):  
Dening Li ◽  
Zheng Zhang
Keyword(s):  
Shock Wave ◽  
Supersonic Flow ◽  
Shock Waves ◽  
Gas Dynamics ◽  
Euler System ◽  
System Of Equations ◽  
Conical Shock ◽  
Compressible Euler ◽  
Isentropic Gas Dynamics ◽  
Isentropic Gas

Conical shock wave is generated when a sharp conical projectile flies supersonically in the air. We study the linear stability and existence of steady conical shock waves in supersonic flow for the equations of complete Euler system in 3D non-isentropic gas-dynamics.

scholarly journals Global existence of a radiative Euler system coupled to an electromagnetic field

2018 ◽  
Vol 8 (1) ◽  
pp. 1158-1170
Author(s):  
Xavier Blanc ◽  
Bernard Ducomet ◽  
Šárka Nečasová
Keyword(s):  
Cauchy Problem ◽  
Electromagnetic Field ◽  
Global Existence ◽  
Smooth Solution ◽  
Euler System ◽  
Singular Limit ◽  
System Of Equations ◽  
Global Smooth Solution ◽  
Compressible Euler ◽  
The Cauchy Problem

Abstract We study the Cauchy problem for a system of equations corresponding to a singular limit of radiative hydrodynamics, namely, the 3D radiative compressible Euler system coupled to an electromagnetic field. Assuming smallness hypotheses for the data, we prove that the problem admits a unique global smooth solution and study its asymptotics.

scholarly journals Riser and well casing analysis during drift-off: a coupled solution in the time domain

2022 ◽  
Author(s):  
Fabiano Guimarães
Keyword(s):  
Time Domain ◽  
Finite Differences ◽  
Coupled System ◽  
Computational Effort ◽  
System Of Equations ◽  
Recursive Method ◽  
Coupled Equations ◽  
The Time Domain ◽  
The Impact ◽  
Fully Coupled

AbstractOne of the most serious incidents that can occur in offshore drilling and exploration is damage to the well structure and subsea components which can result in uncontrolled hydrocarbon release to the environment and present a safety hazard to rig personnel. Over decades, there have been substantial developments to the mathematical models and algorithms used to analyze the stresses on the related structure and to define the operational and integrity windows in which operations can proceed safely and where the mechanical integrity of the well is preserved. The purpose of this work is to present a time-domain solution to the system of equations that model the dynamic behavior of the riser and casing strings, when connected for well drilling/completion during the event of drift-off of the rig. The model combines a solution using finite differences for the riser dynamics and a recursive method to analyze the behavior of the casing in the soil. It allows for the coupling between the equations related to the riser and casing and for the coupling with the equations that describe the dynamics of the rig when station keeping capabilities are lost. The use of the forward–backward finite-differences coupled with the recursive method does not require linearization of the forces acting on the structure making it an ideal methodology for riser analysis while improving convergence. The findings of this study can help improve understanding of the impact of the watch circle limits to riser/well integrity, whether these limits are set based on a quasi-static drive-off/drift-off or fully dynamic. The gain in accuracy in using the fully coupled equations of drift-off dynamics, where there is interaction between the rig and the top of the riser during drive-off/drift-off, is evaluated, and the effects of varying the riser top tension and the compressive loads on the casing string are also analyzed. In particular, it is shown that the results of the fully coupled system of equations representing the dynamics of the riser and casing during drift-off/drive-off are less conservative than the quasi-static approach. Another important finding is that the gain in accuracy in coupling the top of the riser and the rig during drift-off/drive-off is not substantial, which indicates that solving separately the rig dynamics equations and the riser-casing equations is an approach that provides reasonable results with less computational effort. The model can also be used to evaluate wellhead and casing fatigue during the life of the intervention. Finally, the model limitations are discussed.

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