Spectral methods in time for parabolic problems
SIAM Journal on Numerical Analysis
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
| Hi-index | 31.45 |
We design a numerical algorithm for simulation of low-frequency electric-signal transmission through a drill string. This is represented by a transmission line with varying geometrical and electromagnetic properties versus depth, depending on the characteristics of the drill-string/formation system. These properties are implicitly modeled by the series impedance and the shunt admittance of the transmission line. The differential equations are parabolic, since at low frequencies the wave field is diffusive. We use an explicit scheme for the solution of parabolic problems, based on a Chebyshev expansion of the evolution operator and the Fourier pseudospectral method to compute the spatial derivatives. The results are verified by comparison to analytical solutions obtained for the initial-value problem with a voltage source.