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Implicit boundary condition
Posted Jun 4, 2013, 7:01 a.m. EDT Version 4.3a 1 Reply
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Hello,
I am trying to solve a set of reaction-diffusion equations and the heat equation, using general form PDE.
On one boundary some of the boundary fluxes depend on a quantity (electrochemical potential) that is the solution a transcendental equation involving boundary values of the dependent variables (concentrations and temperature). Because I have to use the time-discrete solver, the previous step values of boundary concentrations and temperature could be used in this transcendental equation.
I cannot figure out how (where in the model) to set up this transcendental equation.
I was trying to define this electrochemical potential as a variable defined on a boundary, but it seems that the expression defining this variable cannot be an implicit equation.
Using this equation as an additional boundary constraint produced no formal complaints, but the execution stopped after about 2.8e8 s with "Nonlinear solver did not converge".
Any other ideas?
Thanks in advance,
Miroslav
I am trying to solve a set of reaction-diffusion equations and the heat equation, using general form PDE.
On one boundary some of the boundary fluxes depend on a quantity (electrochemical potential) that is the solution a transcendental equation involving boundary values of the dependent variables (concentrations and temperature). Because I have to use the time-discrete solver, the previous step values of boundary concentrations and temperature could be used in this transcendental equation.
I cannot figure out how (where in the model) to set up this transcendental equation.
I was trying to define this electrochemical potential as a variable defined on a boundary, but it seems that the expression defining this variable cannot be an implicit equation.
Using this equation as an additional boundary constraint produced no formal complaints, but the execution stopped after about 2.8e8 s with "Nonlinear solver did not converge".
Any other ideas?
Thanks in advance,
Miroslav
1 Reply Last Post Jun 10, 2013, 2:54 a.m. EDT
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Posted:
1 decade ago
Hi again,
To make clear my problem, I have attached here the simplified version on my 1D model.
In Global Definitions, Functions, please note the last three functions called iAbase, iCbase and iDbase.
There are used in the boundary conditions of General PDE 1 (cDiff), at the left boundary.
Here the following condition has to be satisfied:
2*iAbase(T,Ee) + iCbase(T,Ee,c5) + iDbase(T,Ee) = 0 (1)
Here Ee is the electrochemical potential mentioned in my previous post. It's value is the solution of the above equation (1). Thus it is a function of values of temperature T and concentration c5 at the left boundary.
I have tried to define Ee in Model 1, Definitions, Variables, Variables 8a, as a variable defined on boundary only.
Equation (1) is then solved in Pointwise Constraint 1 (of Boundary conditions of General PDE 1), at least that's how I hoped it will be solved.
The value of Ee that was supposed to be obtained in this way is then used in Constraint 2.
This setup apparently does not work as intended. I would really appreciate any help in how this problem should be solved properly.
Thanks again,
Miroslav
P.S. In the global definitions, many parameters and functions are left that are not used in the simplified model.
To make clear my problem, I have attached here the simplified version on my 1D model.
In Global Definitions, Functions, please note the last three functions called iAbase, iCbase and iDbase.
There are used in the boundary conditions of General PDE 1 (cDiff), at the left boundary.
Here the following condition has to be satisfied:
2*iAbase(T,Ee) + iCbase(T,Ee,c5) + iDbase(T,Ee) = 0 (1)
Here Ee is the electrochemical potential mentioned in my previous post. It's value is the solution of the above equation (1). Thus it is a function of values of temperature T and concentration c5 at the left boundary.
I have tried to define Ee in Model 1, Definitions, Variables, Variables 8a, as a variable defined on boundary only.
Equation (1) is then solved in Pointwise Constraint 1 (of Boundary conditions of General PDE 1), at least that's how I hoped it will be solved.
The value of Ee that was supposed to be obtained in this way is then used in Constraint 2.
This setup apparently does not work as intended. I would really appreciate any help in how this problem should be solved properly.
Thanks again,
Miroslav
P.S. In the global definitions, many parameters and functions are left that are not used in the simplified model.
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