This paper concerns with the analysis of an iterative procedure for the solution of a nonlinear nonstationary diffusion convection equation in a two dimensional bounded domain supplemented by Dirichlet boundary conditions. This procedure, denoted Lagged Diffusivity method, computes the solution by lagging the diffusion term. A model problem is considered and a finite difference discretization for that model is described. Furthermore, properties of the finite difference operator are proved. Then, a sufficient condition for the convergence of the Lagged Diffusivity method is given. At each stage of the iterative procedure a linear system has to be solved and the Arithmetic Mean method is used. Numerical experiments show the efficiency, for different test functions, of the Lagged Diffusivity methodcombined with the Arithmetic Mean method as inner solver. Better results are obtained when the convection term increases.

Galligani, Emanuele. "Lagged diffusivity method for the solution of nonlinear diffusion convection problems with finite differences" Working paper, Dipartimento di Ingegneria Enzo Ferrari - Università di Modena e Reggio Emilia, 2011. https://doi.org/10.25431/11380_741064

Lagged diffusivity method for the solution of nonlinear diffusion convection problems with finite differences

GALLIGANI, Emanuele
2011

Abstract

This paper concerns with the analysis of an iterative procedure for the solution of a nonlinear nonstationary diffusion convection equation in a two dimensional bounded domain supplemented by Dirichlet boundary conditions. This procedure, denoted Lagged Diffusivity method, computes the solution by lagging the diffusion term. A model problem is considered and a finite difference discretization for that model is described. Furthermore, properties of the finite difference operator are proved. Then, a sufficient condition for the convergence of the Lagged Diffusivity method is given. At each stage of the iterative procedure a linear system has to be solved and the Arithmetic Mean method is used. Numerical experiments show the efficiency, for different test functions, of the Lagged Diffusivity methodcombined with the Arithmetic Mean method as inner solver. Better results are obtained when the convection term increases.
2011
Agosto
TR NA-UniMoRE-3-2011
Galligani, Emanuele
Galligani, Emanuele. "Lagged diffusivity method for the solution of nonlinear diffusion convection problems with finite differences" Working paper, Dipartimento di Ingegneria Enzo Ferrari - Università di Modena e Reggio Emilia, 2011. https://doi.org/10.25431/11380_741064
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/741064
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