team:gdeliege:espaint
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| team:gdeliege:espaint [2015/08/12 11:38] – geoffrey | team:gdeliege:espaint [2016/03/30 15:23] (current) – external edit 127.0.0.1 | ||
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| - | ==== Electrostatic painting ==== | + | ===== Electrostatic painting |
| - | == Problem description == | + | === Problem description |
| Electrostatic painting is one of the applications I studied during my PhD. | Electrostatic painting is one of the applications I studied during my PhD. | ||
| - | I started from a mathematical model by François Henrotte | + | I started from a mathematical model by François Henrotte |
| and used this nice coupled problem to test different potential and mixed formulations | and used this nice coupled problem to test different potential and mixed formulations | ||
| of electrostatic equations. | of electrostatic equations. | ||
| Line 27: | Line 27: | ||
| It must be noted that electrostatic and magnetostatic mixed formulations have the same stability problems as Stokes equations when the shape functions do not satisfy the Babuska-Brezzi inf-sup condition. | It must be noted that electrostatic and magnetostatic mixed formulations have the same stability problems as Stokes equations when the shape functions do not satisfy the Babuska-Brezzi inf-sup condition. | ||
| Fortunately, | Fortunately, | ||
| + | |||
| + | === Finite element simulations === | ||
| The geometrical model is a box extending from the middle of a wire to half the distance between two consecutive wires (Fig. 1). | The geometrical model is a box extending from the middle of a wire to half the distance between two consecutive wires (Fig. 1). | ||
| Line 42: | Line 44: | ||
| //Figure 3. Finite element simulation results : (left) current flowing through the wire and plate surfaces, (right) error on the charge conservation at each time step, calculated as the relative difference between the total charge variation during a time step and the integral of the currents on the wire and plate surfaces.// | //Figure 3. Finite element simulation results : (left) current flowing through the wire and plate surfaces, (right) error on the charge conservation at each time step, calculated as the relative difference between the total charge variation during a time step and the integral of the currents on the wire and plate surfaces.// | ||
| + | === References === | ||
| - | == References == | + | [1] F. Henrotte. //Calcul des efforts électromagnétiques et de leurs effets dans des structures quelconques// |
| - | + | [2] G. Deliége, F. Henrotte, W. Deprez, K. Hameyer. //Finite element modelling of ion convection by electrostatic forces.// IET Science, Measurement & Technology, vol. 151, pp. 398-402, 2004 \\ | |
| - | [1] F. Henrotte. //Calcul des efforts électromagnétiques et de leurs effets dans des structures quelconques// | + | [3] G. Deliége, E. Rosseel, S. Vandewalle. //Iterative solvers and stabilisation for mixed electrostatic and magnetostatic formulations.// |
| - | [2] G. Deliége, F. Henrotte, W. Deprez, K. Hameyer. //Finite element modelling of ion convection by electrostatic forces.// IET Science, Measurement & Technology, vol. 151, pp. 398-402, 2004. | + | \\ |
| - | [3] G. Deliége, E. Rosseel, S. Vandewalle. //Iterative solvers and stabilisation for mixed electrostatic and magnetostatic formulations.// | + | [[team: |
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