Method of Characteristics First-Order Equations

2018 ◽  
pp. 49-87
Keyword(s):  
Method Of Characteristics ◽  
First Order

A Comparative Study of Numerical Techniques for Nonequilibrium Method of Characteristics

1992 ◽  
Author(s):  
T. Gary Yip ◽  
David M. Crook ◽  
Timothy P. Buell
Keyword(s):  
Method Of Characteristics ◽  
Solution Process ◽  
Initial Pressure ◽  
Single Step ◽  
Supersonic Combustion ◽  
Duct Flow ◽  
Unit Process ◽  
First Order ◽  
Constant Area ◽  
Fifth Order

Abstract Three techniques which employ different approaches for obtaining a method of characteristics solution for chemical non-equilibrium flows are reviewed and compared. Two features of the solution process are evaluated to determine their effect on the accuracy of the solution. The first aspect to be considered is the integration of the stiff conservation equations in a unit process. A new fifth-order accurate, multi-step integration routine is contrasted with a first-order accurate, single-step forward differencing scheme. The second comparison is designed to determine if a solution of the flowfield along continuous streamlines is superior to one along discontinuous segments of the streamlines. Tests are performed, using a chemical model describing the supersonic combustion of H2-air. Calculations of single unit processes are used to validate the techniques and to determine suitable grid sizes. Solutions for constant area duct flow show that the techniques which use the multi-step integration routine are more accurate. Results from the constant area duct test, for an initial pressure of 3.685 atm, show that a method of characteristics technique which utilizes continuous streamlines is able to converge at a grid size two orders of magnitude larger than that needed by a technique which uses discontinuous segments of streamlines.

Wheel-Wear Compensation for Numerical Form Grinding

1986 ◽  
Vol 108 (1) ◽  
pp. 16-21 ◽  
Author(s):  
T. Giridharan ◽  
R. C. Dix ◽  
S. Nair
Keyword(s):  
Method Of Characteristics ◽  
Grinding Wheel ◽  
Surfaces Of Revolution ◽  
Wheel Wear ◽  
Closed Form Solutions ◽  
First Order ◽  
Grinding Wheel Wear ◽  
Form Grinding ◽  
Wheel Profile ◽  
Wheel Wear Compensation

A new method for reducing the effect of grinding wheel wear on workpiece inaccuracy in numerically controlled form grinding of surfaces of revolution is proposed and analyzed. A mathematical model to describe wheel wear and contour production is developed for the grinding of a cyclindrical surface. The model results in a first-order hyperbolic differential equation for the radius of the wheel profile as a function of time and position. This equation is solved numerically using the method of characteristics. Closed-form solutions are also presented for a simplifed version of this equation. Pertinent results, such as reduction in the error in the workpiece radius, are presented to demonstrate the effectiveness of the proposed method.

Optimal control of a hyperbolic system that describes Slutsky demand

2021 ◽  
pp. 58-59
Author(s):  
Olha Milchenko
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Hyperbolic System ◽  
Method Of Characteristics ◽  
Social Processes ◽  
Computational Algorithms ◽  
Initial Condition ◽  
Linear Optimal Control ◽  
First Order

A non-linear optimal control problem for a hyperbolic system of first order equations on a line in the case of degeneracy of the initial condition line is considered. This problem describes many natural, economic and social processes, in particular, the optimality of the Slutsky demand, the theory of bio-population, etc. The research is based on the method of characteristics and the use of nonstandard variations of the increment of target functional, which leads to the construction of efficient computational algorithms.

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