Solving the Laplace Tidal Equations using Freely Available, Easily Extensible Finite Element Software
| Autor: | Vlad Constantin Manea, E. G. Sewell |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Laplace transform
Computer science media_common.quotation_subject 0208 environmental biotechnology Tidal heating 02 engineering and technology Dissipation 010502 geochemistry & geophysics Icy moon 01 natural sciences Finite element method 020801 environmental engineering Piecewise Applied mathematics Astrophysics::Earth and Planetary Astrophysics Computers in Earth Sciences Eccentricity (behavior) Enceladus 0105 earth and related environmental sciences Information Systems media_common |
| Zdroj: | Computers & Geosciences. 155:104865 |
| ISSN: | 0098-3004 |
| Popis: | The Laplace Tidal Equations (LTEs) play a basic role for investigating the dissipation of long-term orbital energy as heat in surface oceans of icy satellites. Here we address solving LTEs by means of finite elements using PDE2D, a general-purpose finite element program for solving multidimensional PDEs. We use PDE2D to solve the equations for eccentricity and obliquity gravitational potentials for a shallow water approximation, and calculate ocean dissipation in three icy satellites, Enceladus, Europa and Titan. Compared with previous modeling procedures, PDE2D solves for unknowns that are approximated by piecewise cubic polynomials, thus attaining a higher O(dφ4) + O(dθ4) numerical precision. Our modeling results show, within few percent errors, a good agreement with earlier semi-analytical models and numerical solutions. We provide an open access to our PDE2D codes which are intended to be simple and easy to adjust for a wide range of tidal heating related problems. Our modeling results show that PDE2D can be a useful tool for researchers studying tidal heating related problems. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect