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Shape functions for velocity interpolation in general hexahedral cells

January 1, 2002

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.

Publication Year 2002
Title Shape functions for velocity interpolation in general hexahedral cells
DOI 10.1023/A:1021218525861
Authors R.L. Naff, T.F. Russell, J. D. Wilson
Publication Type Article
Publication Subtype Journal Article
Series Title Computational Geosciences
Index ID 70023938
Record Source USGS Publications Warehouse