Mimetic Mesh Refinement

A mortar element approach

Master thesis (2012)

Authors

P. Kuystermans Aerospace Engineering

Contributors

M.I. Gerritsma Aerodynamics - Aerospace Engineering (mentor)
R.P. Dwight Aerodynamics - Aerospace Engineering (mentor)
J.J. Kreeft Aerodynamics - Aerospace Engineering (mentor)
P.J. Pinto Rebelo Aerodynamics - Aerospace Engineering (mentor)
Faculty
Aerospace Engineering, Aerospace Engineering
Copyright: © 2012 Peter Kuystermans
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Published Date

14-08-2012

Language

English

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Faculty

Aerospace Engineering

Abstract

This thesis aims to introduce mesh refinement into the Mimetic Spectral Element Method (MSEM). The concept of mimetic discretizations is to mimic the properties of continuous Partial Differential Equations (PDEs) discretely. In many discretization methods information is lost in the actual discretization step which is detrimental to the physical fidelity of the approximated solution. Mimetic methods try to prevent this, a feat achieved by combining the fields of differential geometry and algebraic topology. Where differential geometry describes the continuous problem, algebraic topology functions as its discrete equivalent. By accounting for the spatial and temporal geometric objects each physical quantity is associated with, mimetic methods preserve as much as possible of the continuous structure.