Shape functions for velocity interpolation in general hexahedral cells
Computational Geosciences
By: R.L. Naff, T.F. Russell, and J. D. Wilson
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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.
| 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 |
| Larger Work Title | Computational Geosciences |
| First page | 285 |
| Last page | 314 |
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