A Eulerian-Lagrangian substructuring domain decomposition method for multidimensional, unsteady-state advection-diffusion equations

2002 ◽  
pp. 469-480
Author(s):  
Hong Wang ◽  
Jiangguo Liu ◽  
Magne S. Espedal ◽  
Richard E. Ewing
Keyword(s):  
Domain Decomposition ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Diffusion Equations ◽  
Unsteady State ◽  
Advection Diffusion

ON THE ELLIPTIC-HYPERBOLIC COUPLING I: THE ADVECTION-DIFFUSION EQUATION VIA THE χ-FORMULATION

1993 ◽  
Vol 03 (02) ◽  
pp. 145-170 ◽  
Author(s):  
C. CANUTO ◽  
A. RUSSO
Keyword(s):  
Diffusion Equation ◽  
Domain Decomposition ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Advection Equation ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Subdomain Method ◽  
Self Adaptive

An advection-diffusion equation is considered, for which the solution is advection-dominated in most of the domain. A domain decomposition method based on a self-adaptive, smooth coupling of the reduced advection equation and the full advection-diffusion equation is proposed. The convergence of an iteration-by-subdomain method is investigated.

scholarly journals The mass-conserving domain decomposition method for convection diffusion equations with variable coefficients

2021 ◽  
Author(s):  
Ruiqi Dong ◽  
Zhongguo Zhou ◽  
Xiangdong Chen ◽  
Huiguo Tang ◽  
Qi Zhang
Keyword(s):  
Domain Decomposition ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Variable Coefficients ◽  
Diffusion Equations ◽  
Nonlinear Convection ◽  
Convection Diffusion ◽  
Conserved Domain ◽  
Second Order Convergence ◽  
Interior Solutions

In this paper, a conserved domain decomposition method for solving convection-diffusion equations with variable coefficients is analyzed. The interface fluxes over the sub-domains are firstly obtained by the explicit fluxes scheme. Secondly, the interior solutions and fluxes over each sub-domains are computed by the modified upwind implicit scheme. Then, the interface fluxes are corrected by the obtained solutions. We prove rigorously that our scheme is mass conservative, unconditionally stable and of second-order convergence in spatial step. Numerical examples test the theoretical analysis and efficiencies. Lastly, we extend our scheme to the nonlinear convection-diffusion equations and give the error estimate.

scholarly journals Optimized Domain Decomposition Method for Non Linear Reaction Advection Diffusion Equation

2016 ◽  
Vol 12 (27) ◽  
pp. 63 ◽  
Author(s):  
M.R. Amattouch ◽  
N. Nagid ◽  
H. Belhadj
Keyword(s):  
Diffusion Equation ◽  
Domain Decomposition ◽  
Rate Of Convergence ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Linear Reaction ◽  
Non Linear ◽  
Schwarz Algorithm

This work is devoted to an optimized domain decomposition method applied to a non linear reaction advection diffusion equation. The proposed method is based on the idea of the optimized of two order (OO2) method developed this last two decades. We first treat a modified fixed point technique to linearize the problem and then we generalize the OO2 method and modify it to obtain a new more optimized rate of convergence of the Schwarz algorithm. To compute the new rate of convergence we have used Fourier analysis. For the numerical computation we minimize this rate of convergence using a global optimization algorithm. Several test-cases of analytical problems illustrate this approach and show the efficiency of the proposed new method.

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