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Coupling between PDE and Electrostatics

Posted Nov 22, 2012, 12:32 a.m. EST Low-Frequency Electromagnetics, Plasma Physics, Computational Fluid Dynamics (CFD), Studies & Solvers Version 4.3a 5 Replies

Sin Kim
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Dear All,

Does any one have any experience of solving a steady general form of PDE with steady electrostaics module. I am trying to solve a PDE [ Div(DuE) = 0] where D is the mobility coefficient and E is the electric field vector that is obtained from the solution of [Lap(V) = 0] in order to solve for the space charge distribution (u) within the domain, however I am not getting any meaningful results at all and in some cases not even a solution. I am using the default UMFPACK solver.

Regards
5 Replies Last Post Dec 26, 2016, 4:00 p.m. EST
Pu
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Posted: 1 decade ago Nov 22, 2012, 5:08 a.m. EST
I'm doing some simulation with coupling between RF and PDE modules, but it's clueless from your description.
I'm doing some simulation with coupling between RF and PDE modules, but it's clueless from your description.
Sin Kim
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Posted: 1 decade ago Nov 22, 2012, 9:59 a.m. EST
Hi Zang,

Actually I want to solve the PDE simultaneously with the electrostatic module i.e I need to solve the following two equations :

Laplacian(V)=u/eps eq(1)

Divergence(DuE)=0 eq(2)

where E = -Gradient(V)

D is a contant, eps is a constant and E is actually a vector having two components i.e Ex and Ey V is the voltage field and u is the space charge density. However when I try to solve these equations simultaneously by using UMFPACK solver the simulations do not proceed and immediately reports an error of non symmetric matrix found. I simply cant understand what is wrong and how to solve this problem?




Hi Zang, Actually I want to solve the PDE simultaneously with the electrostatic module i.e I need to solve the following two equations : Laplacian(V)=u/eps eq(1) Divergence(DuE)=0 eq(2) where E = -Gradient(V) D is a contant, eps is a constant and E is actually a vector having two components i.e Ex and Ey V is the voltage field and u is the space charge density. However when I try to solve these equations simultaneously by using UMFPACK solver the simulations do not proceed and immediately reports an error of non symmetric matrix found. I simply cant understand what is wrong and how to solve this problem?
Pu
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Posted: 1 decade ago Nov 22, 2012, 10:02 a.m. EST
It seems the equation system is not complex. But I'm also not familiar with the error message. Perhaps you can upload the model file? I would like to have a look.
It seems the equation system is not complex. But I'm also not familiar with the error message. Perhaps you can upload the model file? I would like to have a look.
Raghuvir J
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Posted: 1 decade ago Apr 11, 2013, 9:44 a.m. EDT
Hello everyone,

I have a convergence problem with modelling of Electrostatics equation coupled with PDE( for charge transport equation). I attached the equations and .mph files.

MODEL : two electrodes placed in domain of air. voltage difference applied. I have to calculate resultant electric field, charge density values and use them to add a body force to laminar flow to simulate plasma.

1. Geometry is simple. Mesh is fine.
2. I tried fully coupled( various damping factors), segregated, parametric sweep of the source term in charge transport equation( which makes it nonlinear) but couldn't get it to converge.
3. I tried using PDEs alone instead of electrostatics,but again same problem ( Plasma Actuator Mod.mph)

Could anyone please help me with way to obtain convergence or any other way to solve the equations attached.
Hello everyone, I have a convergence problem with modelling of Electrostatics equation coupled with PDE( for charge transport equation). I attached the equations and .mph files. MODEL : two electrodes placed in domain of air. voltage difference applied. I have to calculate resultant electric field, charge density values and use them to add a body force to laminar flow to simulate plasma. 1. Geometry is simple. Mesh is fine. 2. I tried fully coupled( various damping factors), segregated, parametric sweep of the source term in charge transport equation( which makes it nonlinear) but couldn't get it to converge. 3. I tried using PDEs alone instead of electrostatics,but again same problem ( Plasma Actuator Mod.mph) Could anyone please help me with way to obtain convergence or any other way to solve the equations attached.
Navid Khordehgah
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Posted: 8 years ago Dec 26, 2016, 4:00 p.m. EST
Hi,

You will need to set a voltage as electrical potential in Electronics Initial Values1 (e.g. 1000V).

Regards,

NK
Hi, You will need to set a voltage as electrical potential in Electronics Initial Values1 (e.g. 1000V). Regards, NK

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