A Finite Element Alternating-Direction Method Combined with a Modified Method of Characteristics for Convection-Diffusion Problems

1989 ◽  
Vol 26 (6) ◽  
pp. 1462-1473 ◽  
Author(s):  
S. V. Krishnamachari ◽  
L. J. Hayes ◽  
T. F. Russell
Keyword(s):  
Finite Element ◽  
Method Of Characteristics ◽  
Alternating Direction Method ◽  
Convection Diffusion ◽  
Modified Method ◽  
Alternating Direction ◽  
Modified Method Of Characteristics ◽  
Diffusion Problems

scholarly journals On the Quasi-monotone Modified Method of Characteristics for Transport-diffusion Problems with Reactive Sources

2001 ◽  
Vol 2 (2) ◽  
pp. 186-210 ◽  
Author(s):  
Mohammed Seaïd
Keyword(s):  
Method Of Characteristics ◽  
Explicit Scheme ◽  
Diffusion Reaction ◽  
Benchmark Problems ◽  
Modified Method ◽  
Nonlinear Reaction ◽  
Modified Method Of Characteristics ◽  
Transport Diffusion ◽  
Real Stability ◽  
Diffusion Problems

AbstractThis is an attempt to construct a strong numerical method for transportdiffusion equations with nonlinear reaction terms, which relies on the idea of the Modified Method of Characteristics that is explicit but stable and is second-order accurate in time. The method consists in convective-diffusive splitting of the equations along the characteristics. The convective stage of the splitting is straightforwardly treated by a quasi-monotone and conservative modified method of characteristics, while the diffusive-reactive stage can be approximated by an explicit scheme with an extended real stability interval. A numerical comparative study of the new method with Characteristics Crank-Nicholson and Classical Characteristics Runge-Kutta schemes, which are used in many transport-diffusion models, is carried out for several benchmark problems, whose solutions represent relevant transport-diffusion-reaction features. Experiments for transport-diffusion equations with linear and nonlinear reactive sources demonstrate the ability of our new algorithm to better maintain the shape of the solution in the presence of shocks and discontinuities.

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