A finite element analysis on fluid motion in librating triaxial ellipsoids. Issue 5 (3rd December 2013)

• Record Type: Journal Article
• Authors: Chan, Kit H.; He, Yinnian; Zhang, Keke; Zou, Jun
• Is Part Of: Numerical methods for partial differential equations. Volume 30:Issue 5(2014:Sep.)
• Page Start: 1518
• Page End: 1537
• Publication Date: 2013-12-03
• Subjects: Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.21833
• Languages: English
• ISSNs: 0749-159X

Abstract

<abstract abstract-type="main"> <title> <x xml:space="preserve">Abstract</x> </title> <p>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 nonconvective. 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 pseudospectral method with the poloidal‐toroidal decomposition is difficult because of nonspherical 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. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1518–1537, 2014</p> </abstract>