7. Method of characteristics for first-order quasilinear equations

2020 ◽  
pp. 157-204
Keyword(s):  
Method Of Characteristics ◽  
Quasilinear Equations ◽  
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.

scholarly journals The nonlocal solvability conditions for a system of two quasilinear equations of the first order with absolute terms

2019 ◽  
Vol 21 (3) ◽  
pp. 317-328
Author(s):  
Marina V. Dontsova
Keyword(s):  
Cauchy Problem ◽  
Finite Number ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
Local Solution ◽  
Quasilinear Equations ◽  
Solvability Conditions ◽  
First Order ◽  
The Cauchy Problem ◽  
Global Estimates

The Cauchy problem for a system of two first-order quasilinear equations with absolute terms is considered. The study of this problem’s solvability in original coordinates is based on the method of an additional argument. The existence of the local solution of the problem with smoothness which is not lower than the smoothness of the initial conditions, is proved. Sufficient conditions of existence are determined for the nonlocal solution that is continued by a finite number of steps from the local solution. The proof of the nonlocal resolvability of the Cauchy problem relies on original global estimates.

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