A Finite Element Analysis on Fluid Motion in Librating Triaxial Ellipsoids
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چکیده
Fluid motion driven by planetary libration may play a key role in maintaining the magnetism of synchronous planets and moons that are thermally or chemically non-convective. We present a fully discrete finite element method on a triaxial ellipsoidal domain for simulating a three-dimensional nonlinear flow in a latitudinally librating triaxial ellipsoidal cavity, for which the usual pseudo-spectral method with the poloidal-toroidal decomposition is difficult because of non-spherical geometry. Stability of the time-dependent finite element solutions with two different temporal schemes are studied, and their error estimates of optimal order are established. The corresponding numerical simulation is implemented for the second-order implicit scheme, offering an insight into the practical aspect of the proposed finite element method.
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تاریخ انتشار 2013