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DEMO_XY / gallery 26: inspired by Stack Exchange, (JohnDow's question), version "in casing", mesh size: 401 x 401 nodes.


Question on forum Physics/Stack Exchange

https://physics.stackexchange.com/questions/113290/simulate-plot-electrostatic-field

Running program

Windows:
DEMO_XY.exe 26

Linux:
./DEMO_XY.run 26

Problem definition.

Numeric meshes

Each pixel of picture represents one mesh node.

white colour - vacuum
red colour   - electrode 1 (casing)
green colour - electrode 2
blue colour  - electrode 3 (round)

Visualization of mesh on picture.

Model parameters

mesh size:

number of rows    ==  401
number of columns ==  401

coordinates:
x_start ==  -200.0 [mm]
x_stop  ==  +200.0 [mm]
y_start ==  -200.0 [mm]
y_stop  ==  +200.0 [mm]

number of iterations

>>> SUCCESS - solution V(x,y) has been found
after 65207 iterations

electrode 1 (red frame, casing)
boundary   ==  1
voltage    ==  +0.0 [V]
thickness  == 10 nodes

electrode 2 (A+B)
(A)
boundary ==  +2
voltage  ==  +9.0 [V]
i_col    ==  181 .. 200
i_row    ==  101 .. 200

(B)
boundary ==  +2
voltage  ==  +9.0 [V]
i_col    ==  101 .. 200
i_row    ==  200 .. 220


electrode 3 (round, blue)
boundary ==  +3
voltage  ==  -1.0   [V]
x_center ==  +50.0  [mm]
y_center ==  +20.0  [mm]
radius   ==  +30.0  [mm]


computation accuracy:
eps ==  1.0E-9 [V]


Computation results


Equipotential lines


Mapping of electrostatic potential [V] to colours

Colormap: grayscale

Colormap: grayscale inverted

Colormap: hot-to-cold

Colormap: hot-to-cold inverted

Colormap: jet

Colormap: jet inverted


Mapping of component x of electric force (E_x) [V/mm] to colours

Important: determinig of exact values of E near electrode surface is generally problematic. These maps have generally illustrative character.

Colormap: grayscale

Colormap: grayscale inverted

Colormap: hot-to-cold

Colormap: hot-to-cold inverted

Colormap: jet

Colormap: jet inverted


Mapping of component y of electric force (E_y) [V/mm] to colours

Important: determinig of exact values of E near electrode surface is generally problematic. These maps have generally illustrative character.

Colormap: grayscale

Colormap: grayscale inverted

Colormap: hot-to-cold

Colormap: hot-to-cold inverted

Colormap: jet

Colormap: jet inverted


Mapping of electric force (E) [V/mm] to colours

algorihm of computation:
E = sqrt(E_x*E_x + E_y*E_y)

Important: determinig of exact values of E near electrode surface is generally problematic. These maps have generally illustrative character.

Colormap: grayscale

Colormap: grayscale inverted

Colormap: hot-to-cold

Colormap: hot-to-cold inverted

Colormap: jet

Colormap: jet inverted


Mapping of square of electric force (E*E == E2) [V2/mm2] to colours

algorithm of computation:
E*E = E_x*E_x + E_y*E_y

Important: determinig of exact values of E near electrode surface is generally problematic. These maps have generally illustrative character.

Colormap: grayscale

Colormap: grayscale inverted

Colormap: hot-to-cold

Colormap: hot-to-cold inverted

Colormap: jet

Colormap: jet inverted


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