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Solving a coupled system of convection-diffusion equation
Posted Jul 29, 2015, 10:31 a.m. EDT Simulation Apps, Mesh, Modeling Tools & Definitions, Parameters, Variables, & Functions, Studies & Solvers Version 4.4, Version 5.0, Version 5.1 2 Replies
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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
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
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2 Replies Last Post Jul 31, 2015, 3:25 a.m. EDT
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Posted:
9 years ago
anyone?
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Posted:
9 years ago
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
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