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.
Suggested Citation
Naff, R., Russell, T., Wilson, J.D., 2002, Shape functions for velocity interpolation in general hexahedral cells: Computational Geosciences, v. 6, no. 3-4, p. 285-314, https://doi.org/10.1023/A:1021218525861.
| 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 |