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Test functions for three-dimensional control-volume mixed finite-element methods on irregular grids

January 1, 2000

Numerical methods based on unstructured grids, with irregular cells, usually 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 and vector test functions are used to minimize the error associated with the numerical approximation scheme. For a logically cubic mesh, the lowest-order shape functions are chosen in a natural way to conserve intercell fluxes that vary linearly in logical space. Vector test functions, while somewhat restricted by the mapping into the logical reference cube, admit a wider class of possibilities. Ideally, an error minimization procedure to select the test function from an acceptable class of candidates would be the best procedure. Lacking such a procedure, we first investigate the effect of possible test functions on the pressure distribution over the control volume; specifically, we look for test functions that allow for the elimination of intermediate pressures on cell faces. From these results, we select three forms for the test function for use in a control-volume mixed method code and subject them to an error analysis for different forms of grid irregularity; errors are reported in terms of the discrete L2 norm of the velocity error. Of these three forms, one appears to produce optimal results for most forms of grid irregularity.

Citation Information

Publication Year 2000
Title Test functions for three-dimensional control-volume mixed finite-element methods on irregular grids
DOI
Authors R.L. Naff, T.F. Russell, J. D. Wilson
Publication Type Conference Paper
Publication Subtype Conference Paper
Series Title
Series Number
Index ID 70023168
Record Source USGS Publications Warehouse
USGS Organization