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Cell shapes suitable for the shift transformation method

Blij, F. van der (2007) Cell shapes suitable for the shift transformation method. Master's Thesis / Essay, Mathematics.

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Abstract

Hicken et al. introduced the use of shift transformations to obtain a fully conservative method on an unstructured Cartesian mesh. In this work, this method is investigated on its possibilities to implement on other unstructured grids, with a main focus on the triangulated mesh. By means of a Taylor series development of the error, a matrix is constituted, which rank is related to the possibility of constructing a second order accurate shift transformation, assuming the underlying velocity field is incompressible. An analysis of the linear dependencies between the rows of this matrix yields the proof of the main theorem of this report. This theorem states that one cannot find such a second order accurate shift transformation on triangles while using its circumcenter as the center of the cell. Furthermore, it is proven that of all the quadrilaterals, only the rectangles are appropriate cell shapes in combination with the circumcenter.

Item Type: Thesis (Master's Thesis / Essay)
Degree programme: Mathematics
Thesis type: Master's Thesis / Essay
Language: English
Date Deposited: 15 Feb 2018 07:28
Last Modified: 15 Feb 2018 07:28
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/8428

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