Institut für Allgemeine Elektrotechnik, Uni Rostock - Universität ...

Limitations of the Leap-Frog Scheme
4. Slowly varying fields ("low-frequency fields", Quasistatics):
wavelength
dimension
(e.g. motors or generators at 50 Hz)
i incident field in conductor has to be modelled by discretization
i matei
r als often non-linear
Example: Copper cube of 10 cm side length inside of cubic
grid of d = 1m side length and uniform step size of 5 mm;
7
conductivity 5.8 ⋅10 S/m, applied alternating current of 50 Hz
⇒ skin depth of δ = 2 / ( ωµ
κ)
≈1cm while vacuum wave
6
length is λ = c / f ≈ 6 ⋅10 m 1 m (grid size).
For the time integration of one period T = 0.02 s the maximal
−12 9
stable time step is Δtmax
≈9.6 ⋅10 s affording 2⋅10 t
Solution:
Implicite time integration scheme
Prof. Dr. Ursula van Rienen, Universität Rostock, Fakultät für Informatik und Elektrotechnik (IEF), Institut für Allgemeine Elektrotechnik (IAE)
ime steps!
7