Shape Functions for Three-Dimensional Control-Volume Mixed Finite-Element Methods on Irregular Grids
GEOLOGICAL SURVEY DENVER CO
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Numerical methods based on unstructured grids, with irregular cells, frequently require discrete shape functions to approximate the distribution of quantities across cells. For control-volume mixed finite-element methods, vector shape functions are used to approximate the distribution of velocities across cells. Previous, two-dimensional developments used linear shape functions to interpolate velocities within a quadrilateral cell. For irregular hexahedral cells in three dimensions, it can be shown that linear shape functions cannot exactly represent the flux distribution across a cell under uniform flow conditions. As a result, uniform flow cannot be exactly simulated. A new vector shape function is proposed for use with irregular hexahedral cells that should provide for a more accurate velocity approximation within a cell. This velocity shape function is a non-linear interpolator, containing quadratic terms.
- Numerical Mathematics
- Fluid Mechanics
- Hydrology, Limnology and Potamology