## About Coordinate Scaling in Elmer Plugin in Salome

General discussion about Elmer
tryphena
Posts: 35
Joined: 16 Apr 2021, 17:38
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### About Coordinate Scaling in Elmer Plugin in Salome

Hello,
I built geometries in Salome and tried to use coordinate scaling factor for FEM analysis in Elmer. I got effective resistance for a box. But I do not know how shall I calculate the resistivity. I know the surface area of the cross section in Salome. Should I multiply the surface area by the coordinate scaling factor once or twice? Please check the following equation. Thank you.

1) Resistivity=[Resistance*S(Electrode cross-section Surface area)*coordinate scaling factor ]/(Length*coordinate scaling factor)=Resistance*S/L
2) Resistivity=[Resistance*S(Electrode cross-section Surface area)*coordinate scaling factor* coordinate scaling factor]/(Length*coordinate scaling factor)=Resistance*S*coordinate scaling factor/L
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annier
Posts: 1157
Joined: 27 Aug 2013, 13:51
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### Re: About Coordinate Scaling in Elmer Plugin in Salome

Hi,
The dimensions of the geometry /mesh exported from Salome do not have any unit, and so the same mesh can be designed in many ways in the FEM simulation.
The distance 603.268 is a unitless number, and so you can imagine it to be of any unit.
Now , if the above unitless length of 603.268 is assumed as mm, then the coordinate scaling = 1.0E-03 sets it to be 0.603268 m.
If it is assumed as 603.268 cm, then the coordinate scaling = 1.0e-02 sets it to be 6.03268 m.
If it is assumed as 603.268 m, then the coordinate scaling = 1.0 sets it to be 603.268 m.
If it is assumed as 603.268 inches, then the coordinate scaling = 2.54e-02 sets it to be 15.323 m in the solver input file.

The concept of coordinate scaling is advantageous, as it is easier to plan for constructing a box of l*b*h = 5.5 *7.3*11.25 (initially designing in mm^3 and later using a coordinate scaling of 1.0e-3) than constructing the same box with l*b*h = 0.0055 *0.0073*0.01125 (initial length construction in m and using coordinate scaling = 1 ).

The general convention is to set the FEM simulation in SI units (through the input of numerical values of materials properties and constants) . The time can be set numerically to be in s (timestep size). A timestep size of 1.0e-3 can be thought to be in any units, and for convention we can choose it to be in SI unit (s) and so it can be understood as 1 ms. It is possible to set time and other units in any other unit values .
The unit of resistivity is ohm m . If the resistivity of Cu is to be set in SI units in Material block, then the numerical value of 1.68*10^(-8). This value corresponds to the unit of ohm m.

Summary: If a geometry of a material at nanoscale is to be contructed in Salome (e.g. sphere of radius 20 nm), then it is good to draw a sphere of r = 20 (unitless), and define it as nm in solver input file by using coordinate scaling of 1.0e-9 . It is a better practice than constructing a sphere of radius r=0.00000002 and using coordinate scaling of 1.0 in solver input file.
Anil Kunwar
Faculty of Mechanical Engineering, Silesian University of Technology, Gliwice