Numerical Integration of the Equations Governing the One-Dimensional Flow of a Chemically Reactive Gas

1969 ◽  
Vol 12 (11) ◽  
pp. 2292 ◽  
Author(s):  
H. E. Bailey
Keyword(s):  
Numerical Integration ◽  
One Dimensional ◽  
Dimensional Flow ◽  
The One ◽  
Reactive Gas

A TWELFTH-ORDER FOUR-STEP FORMULA FOR THE NUMERICAL INTEGRATION OF THE ONE-DIMENSIONAL SCHRÖDINGER EQUATION

2003 ◽  
Vol 14 (08) ◽  
pp. 1087-1105 ◽  
Author(s):  
ZHONGCHENG WANG ◽  
YONGMING DAI
Keyword(s):  
Schrödinger Equation ◽  
Numerical Integration ◽  
Schrodinger Equation ◽  
Numerical Test ◽  
New Method ◽  
Step Method ◽  
One Dimensional ◽  
The Stability ◽  
The One ◽  
Order Four

A new twelfth-order four-step formula containing fourth derivatives for the numerical integration of the one-dimensional Schrödinger equation has been developed. It was found that by adding multi-derivative terms, the stability of a linear multi-step method can be improved and the interval of periodicity of this new method is larger than that of the Numerov's method. The numerical test shows that the new method is superior to the previous lower orders in both accuracy and efficiency and it is specially applied to the problem when an increasing accuracy is requested.

scholarly journals Impact of Energy Slope Averaging Methods on Numerical Solution of 1D Steady Gradually Varied Flow

2015 ◽  
Vol 62 (3-4) ◽  
pp. 101-119 ◽  
Author(s):  
Wojciech Artichowicz ◽  
Dzmitry Prybytak
Keyword(s):  
Numerical Methods ◽  
Numerical Solution ◽  
Numerical Integration ◽  
Cross Sections ◽  
Flow Model ◽  
One Dimensional ◽  
Averaging Methods ◽  
Integration Formulas ◽  
Different Types ◽  
The One

AbstractIn this paper, energy slope averaging in the one-dimensional steady gradually varied flow model is considered. For this purpose, different methods of averaging the energy slope between cross-sections are used. The most popular are arithmetic, geometric, harmonic and hydraulic means. However, from the formal viewpoint, the application of different averaging formulas results in different numerical integration formulas. This study examines the basic properties of numerical methods resulting from different types of averaging.

Theoretical and Computational Analysis of an Auxiliary Power Unit (APU) Installation Cooling System

2012 ◽  
Author(s):  
Parthiv N. Shah ◽  
Tricia Waniewski Sur ◽  
R. Scott Miskovish ◽  
Albert Robinson
Keyword(s):  
Network Model ◽  
Cooling System ◽  
Dimensional Model ◽  
Ambient Conditions ◽  
Modeling Framework ◽  
Flow Network ◽  
One Dimensional ◽  
Dimensional Flow ◽  
System Pressure ◽  
The One

This paper presents a theoretical one-dimensional model and computational fluid dynamics (CFD) simulations of a tailcone-installed APU cooling system. The work is motivated by the need to deliver sufficient cooling airflow to critical components within an aircraft tailcone compartment. The cooling system considered herein utilizes (1) an eductor system at the APU exhaust and (2) a ram air scoop near an upstream inlet to the compartment to induce the necessary cooling flow during ground and in-flight APU operation. A one-dimensional flow network model provides a framework for the quantification and matching of eductor pumping and system pressure drop characteristics. Detailed CFD models that simulate internal tailcone compartment flows driven by ambient conditions external to the aircraft in ground or flight operation support the one-dimensional model and are used to characterize component performance and assess different scoop and eductor designs. The one-dimensional flow network model is calibrated to the CFD results to predict system cooling performance under known APU loads at points on the ground and in the flight envelope. The agreement between the models is encouraging and suggests the modeling framework and CFD techniques discussed will be applicable to future designs and improvements of eductor-driven aircraft compartment cooling systems.

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