A lagged diffusivity method for reaction–convection–diffusion equations with Dirichlet boundary conditions

2018 ◽  
Vol 123 ◽  
pp. 300-319 ◽  
Author(s):  
Francesco Mezzadri ◽  
Emanuele Galligani
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Diffusion Equations ◽  
Convection Diffusion

FACTORIZATION OF THE CONVECTION-DIFFUSION OPERATOR AND THE SCHWARZ ALGORITHM

1995 ◽  
Vol 05 (01) ◽  
pp. 67-93 ◽  
Author(s):  
F. NATAF ◽  
F. ROGIER
Keyword(s):  
Boundary Conditions ◽  
Rate Of Convergence ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Interface Conditions ◽  
Diffusion Operator ◽  
Convection Diffusion ◽  
Numerical Tests ◽  
Schwarz Algorithm ◽  
Theoretical Results

In the original Schwarz algorithm, Dirichlet boundary conditions are used as interface conditions. We consider the use of the operators arising from the factorization of the convection-diffusion operator as transmission conditions. The rate of convergence is then significantly higher. Theoretical results are proven and numerical tests are shown.

Universal Parallel Solver for Convection-Diffusion Equations

2004 ◽  
Vol 14 (01) ◽  
pp. 107-117
Author(s):  
XIAOLI ZHI ◽  
RONG LU ◽  
XINDA LU
Keyword(s):  
Dirichlet Boundary ◽  
Three Dimensional ◽  
Software Tool ◽  
Dirichlet Boundary Conditions ◽  
Diffusion Equations ◽  
Fractional Step ◽  
Unconditionally Stable ◽  
Convection Diffusion ◽  
Parallel Solver ◽  
Iteration Technique

A parallel unconditionally stable solver for three-dimensional convection-diffusion equations is proposed by applying the upwind Crank-Nicolson difference schemes combined with alternating bar parallelization. This solver can be applied numerically to any variation of convection-diffusion equations with Dirichlet boundary conditions. Making use of a fractional step iteration technique for linear systems, this approach yields good runtime performance. To validate the accuracy and efficiency of the method, sample experiments are done on a software tool, Codie4D, which was implemented using the MPICH library.

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