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Solving a coupled system of convection-diffusion equation

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Hi all,

I am having trouble solving two coupled pdes, its described below

I have a 2d system (square) and from the top boundary a nutrient (C) flows in to the square. I have set the concentration S=S0 at the top boundary. The nutrient is defined as a convection diffusion equation

secondly I have cells (Pinit=0.1) inside the square modelled as a convection-diffusion equation.

\frac{\partial P }{\partial t}=D_p\triangledown P + K_bCP,
\frac{\partial C }{\partial t}=D_o\triangledown C + \lambda_oPC

I want to solve C using the initial value of P(Pinit) then to solve P using C.

I want to repeat the process till the system reaches steady state.

I don't know how to solve a coupled system in cosmos 5.1 or 4.4 (newer versions)

Please help me. attached is a screen shot of the equations


2 Replies Last Post 31.07.2015, 03:25 GMT-4

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Posted: 9 years ago 30.07.2015, 02:03 GMT-4
anyone?
anyone?

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Posted: 9 years ago 31.07.2015, 03:25 GMT-4
Hi

First, I cannot understand your equations, there is no convection term and in the diffusion term you should have nabla square (delta) instead of nabla. Reaction term coefficient lambda_0 should be negative if the nutrient is consumed by the cells.

I would use Transport of Diluted Species physics to solve this problem because it would be much easier. Unless you have your reasons of having exactly those equations (then D's are not diffusion coefficients).

BR
Lasse
Hi First, I cannot understand your equations, there is no convection term and in the diffusion term you should have nabla square (delta) instead of nabla. Reaction term coefficient lambda_0 should be negative if the nutrient is consumed by the cells. I would use Transport of Diluted Species physics to solve this problem because it would be much easier. Unless you have your reasons of having exactly those equations (then D's are not diffusion coefficients). BR Lasse

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