Applications of the Numerical Method of Lines (NMOL) in Soil Hydrology

1987 ◽  
Vol 30 (1) ◽  
pp. 0198-0201 ◽  
Author(s):  
Shiv O. Prasher ◽  
Chandra Madramootoo
Keyword(s):  
Numerical Method ◽  
Method Of Lines ◽  
Soil Hydrology

A Numerical Study of Nonaxisymmetric Stokesian Flow in a Circular Tube

1981 ◽  
Vol 48 (3) ◽  
pp. 459-464
Author(s):  
J. Strigberger ◽  
A. Plotkin
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Circular Tube ◽  
Numerical Study ◽  
Mathematical Problem ◽  
Method Of Lines ◽  
Tube Axis ◽  
First Order ◽  
The Method Of Lines ◽  
Fixed Radius

A numerical study of the nonaxisymmetric Stokesian flow of a Newtonian fluid in a rigid circular tube of fixed radius has been performed. The analysis presented here is an integral part of the problem of modeling the flow of blood near the ostia of the intercostal arteries of rabbits in order to study a possible factor in the initiation of atherosclerosis. The method of lines is used to reduce the mathematical problem to one of solving a system of first-order ordinary differential equations along lines parallel to the tube axis. Solutions are obtained analytically using matrix eigenvalue techniques for the first two Fourier components of the flow and the accuracy of the numerical method is verified by suitable comparison with the results of independent computations.

Feedback Control of Heat Transfer Systems by the Numerical Method of Lines

2009 ◽  
Author(s):  
David Brown ◽  
Chao Zhang ◽  
Jin Jiang
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Numerical Method ◽  
Direct Method ◽  
Method Of Lines ◽  
Finite Volume Methods ◽  
Current State ◽  
Heat Transfer System ◽  
Ordinary Time ◽  
Feedback Optimal Control

A direct method for feedback optimal control of fluid flow and heat transfer systems is investigated. The method consists of discretizing the spatial component of the governing partial differential equations using standard finite-volume methods (FVM) while leaving the transient term in its differential form. This partial discretization method is commonly known as the Numerical Method of Lines (NUMOL). The control is then applied to the partially discretized system of linear ordinary time differential equations. Of particular interest is the effectiveness of linearizing about the current state rather than the origin. The effectiveness of this method is investigated through numerical implementation on a simple one-dimensional heat transfer system.

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