Shape Functions for Three-Dimensional Control-Volume Mixed Finite-Element Methods on Irregular Grids
Abstract
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 2002
- Accession Number
- ADA445725
Entities
People
- John D. Wilson
- Richard L. Naff
- Thomas F. Russell