Solving the Poisson Equation in complex situations

celestial · July 26, 2021, 10:34

Hello everybody

This is a question on electromagnetism as opposed to fluid dynamics.

Imagine we have several regions of different dielectric constants with one region having a known charge distribution and some boundaries between regions having a preassigned potential and others having a known surface charge distribution.
What then is the most efficient way in OpenFoam to solve the Poisson equation over the entire domain ?
Or is finite element software more suitable for that task ?

Thanks for your time reading this. Any reply appreciated.

piu58 · July 26, 2021, 12:02

The potential equation is best simulated by boundary elements. This is not included in OpenFoam.
Two advantages:
- you need only to mesh the boundaries
- it is easy the get high flux rates (current density for the flow field). This is always a problem with FEM / FDM.

The principle is to cover the boundaries with some kind of point charges. The mathematisch behind the BEM avoid the singularity which arises if source and control points are identical.

celestial · July 29, 2021, 00:54

Thanks, Uwe, for the BEM tip. I was actually using the FEM software Elmer for over a year and I was aware it had A BEM model for the Poisson equation under their experimental and obsolete solvers section of their manual. So, I ignored it and instead implemented my version of their static electricity FEM solver. However, my research being on surface dielectric barrier discharge wing actuators also involves the continuity equations for 3 different ions as well as the Navier-Stokes equations for air. I now wonder if I better interface Elmer to OpenFoam as I had yet no luck in simulations of all these plasma equations using either Elmer or OpenFoam separately.

Regards, Marc

July 26, 2021, 10:34	Solving the Poisson Equation in complex situations	#1
celestial Member Join Date: Mar 2019 Posts: 86 Rep Power: 7	Hello everybody This is a question on electromagnetism as opposed to fluid dynamics. Imagine we have several regions of different dielectric constants with one region having a known charge distribution and some boundaries between regions having a preassigned potential and others having a known surface charge distribution. What then is the most efficient way in OpenFoam to solve the Poisson equation over the entire domain ? Or is finite element software more suitable for that task ? Thanks for your time reading this. Any reply appreciated.

July 26, 2021, 12:02		#2
piu58 Senior Member Uwe Pilz Join Date: Feb 2017 Location: Leipzig, Germany Posts: 744 Rep Power: 15	The potential equation is best simulated by boundary elements. This is not included in OpenFoam. Two advantages: - you need only to mesh the boundaries - it is easy the get high flux rates (current density for the flow field). This is always a problem with FEM / FDM. The principle is to cover the boundaries with some kind of point charges. The mathematisch behind the BEM avoid the singularity which arises if source and control points are identical. __________________ Uwe Pilz -- Die der Hauptbewegung überlagerte Schwankungsbewegung ist in ihren Einzelheiten so hoffnungslos kompliziert, daß ihre theoretische Berechnung aussichtslos erscheint. (Hermann Schlichting, 1950)

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July 29, 2021, 00:54		#3
celestial Member Join Date: Mar 2019 Posts: 86 Rep Power: 7	Thanks, Uwe, for the BEM tip. I was actually using the FEM software Elmer for over a year and I was aware it had A BEM model for the Poisson equation under their experimental and obsolete solvers section of their manual. So, I ignored it and instead implemented my version of their static electricity FEM solver. However, my research being on surface dielectric barrier discharge wing actuators also involves the continuity equations for 3 different ions as well as the Navier-Stokes equations for air. I now wonder if I better interface Elmer to OpenFoam as I had yet no luck in simulations of all these plasma equations using either Elmer or OpenFoam separately. Regards, Marc