An explicit characteristic finite volume element method for non-divergence free convection–diffusion-reaction equation

2012 ◽  
Vol 4 (3) ◽  
pp. 179-192
Author(s):  
S. Phongthanapanich ◽  
P. Dechaumphai
Keyword(s):  
Free Convection ◽  
Finite Volume ◽  
Volume Element ◽  
Diffusion Reaction ◽  
Reaction Equation ◽  
Finite Volume Element Method ◽  
Convection Diffusion ◽  
Finite Volume Element ◽  
Divergence Free ◽  
Element Method

A CHARACTERISTIC-BASED FINITE VOLUME ELEMENT METHOD FOR CONVECTION-DIFFUSION-REACTION EQUATION

2008 ◽  
Vol 32 (3-4) ◽  
pp. 549-560 ◽  
Author(s):  
Sutthisak Phongthanapanich ◽  
Pramote Dechaumphai
Keyword(s):  
Finite Volume ◽  
Numerical Solutions ◽  
Volume Element ◽  
Diffusion Reaction ◽  
Solution Stability ◽  
Reaction Equation ◽  
Finite Volume Element Method ◽  
Convection Diffusion ◽  
Finite Volume Element ◽  
Element Method

A two-dimensional convection-diffusion-reaction equation is discretized by the finite volume element method on triangular meshes. Time-dependent convection-diffusion-reaction equation is developed along the characteristic path using the characteristic-based scheme, while the finite volume method is employed for deriving the discretized equations. The concept of the finite element technique is applied to estimate the gradient quantities at the cell faces of the finite volume. Numerical test cases have shown that the method does not require any artificial diffusion to improve the solution stability. The robustness and the accuracy of the method have been evaluated by using available analytical and numerical solutions of the pure-convection, convection-diffusion and convection-diffusion-reaction problems.

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