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Shape functions for velocity interpolation in general hexahedral cells

Computational Geosciences

By:
, ,
DOI: 10.1023/A:1021218525861

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Abstract

Numerical methods for grids with irregular cells require discrete shape functions to approximate the distribution of quantities across cells. For control-volume mixed finite-element (CVMFE) methods, vector shape functions approximate velocities and vector test functions enforce a discrete form of Darcy's law. In this paper, a new vector shape function is developed for use with irregular, hexahedral cells (trilinear images of cubes). It interpolates velocities and fluxes quadratically, because as shown here, the usual Piola-transformed shape functions, which interpolate linearly, cannot match uniform flow on general hexahedral cells. Truncation-error estimates for the shape function are demonstrated. CVMFE simulations of uniform and non-uniform flow with irregular meshes show first- and second-order convergence of fluxes in the L2 norm in the presence and absence of singularities, respectively.

Additional Publication Details

Publication type:
Article
Publication Subtype:
Journal Article
Title:
Shape functions for velocity interpolation in general hexahedral cells
Series title:
Computational Geosciences
DOI:
10.1023/A:1021218525861
Volume
6
Issue:
3-4
Year Published:
2002
Language:
English
Larger Work Type:
Article
Larger Work Subtype:
Journal Article
First page:
285
Last page:
314
Number of Pages:
30