Construction of the solutions of a system of boundary-layer equations by the method of lines with respect to time

1982 ◽  
pp. 123-141
Author(s):  
D. A. Silaev
Keyword(s):  
Boundary Layer ◽  
Method Of Lines ◽  
Boundary Layer Equations ◽  
The Method Of Lines

SOLUTION OF THE RICHARDS EQUATION IN A SOIL PROFILE WITH TWO LAYERS USING THE METHOD OF LINES

2020 ◽  
Author(s):  
Diego Sousa Lopes ◽  
Augusto Cezar Cordeiro Jardim ◽  
Diego Estumano ◽  
Emanuel Macêdo ◽  
João Quaresma
Keyword(s):  
Soil Profile ◽  
Method Of Lines ◽  
Richards Equation ◽  
The Method Of Lines

Numerical studies of the hypersonic strong interaction boundary-layer equations

AIAA Journal ◽  
1971 ◽  
Vol 9 (10) ◽  
pp. 2058-2060 ◽  
Author(s):  
M. J. WERLE ◽  
S. F. WORNOM
Keyword(s):  
Boundary Layer ◽  
Strong Interaction ◽  
Boundary Layer Equations ◽  
Numerical Studies

TRAVELLING WAVES AND OSCILLATIONS IN SAL’NIKOV’S COMBUSTION REACTION IN A COMPRESSIBLE GAS

2015 ◽  
Vol 56 (3) ◽  
pp. 233-247 ◽  
Author(s):  
RHYS A. PAUL ◽  
LAWRENCE K. FORBES
Keyword(s):  
Asymptotic Solution ◽  
Multiple Scales ◽  
Travelling Waves ◽  
Method Of Lines ◽  
Travelling Wave ◽  
Reaction Scheme ◽  
Compressible Viscous Gas ◽  
The Method Of Lines ◽  
Temperature Waves ◽  
Parameter Values

We consider a two-step Sal’nikov reaction scheme occurring within a compressible viscous gas. The first step of the reaction may be either endothermic or exothermic, while the second step is strictly exothermic. Energy may also be lost from the system due to Newtonian cooling. An asymptotic solution for temperature perturbations of small amplitude is presented using the methods of strained coordinates and multiple scales, and a travelling wave solution with a sech-squared profile is derived. The method of lines is then used to approximate the full system with a set of ordinary differential equations, which are integrated numerically to track accurately the evolution of the reaction front. This numerical method is used to verify the asymptotic solution and investigate behaviours under different conditions. Using this method, temperature waves progressing as pulsatile fronts are detected at appropriate parameter values.

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