Geology topics

J. D. Wilson

Publications and source records attributed to J. D. Wilson.

3 recordsLinked to original sources

USGS2002

Shape functions for velocity interpolation in general hexahedral cells

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.

Computational Geosciences↗

USGS2000

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

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.

Conference Paper↗

USGS1981

Modification of the Tangborn short-term hydrometeorological model, with trial results from the Baker River basin, Washington

This report presents a modification of the short-term hydrometeorological model (Tangborn, 1978) for estimating river-basin snowmelt runoff. A multiple linear regression replaces a nonlinear regression scheme to correct for temperature effects of snowmelt runoff. Results based on data from the Baker River basin, Washington, indicate that model performance is improved by the modification in a majority of applications, and, additionally, use of the model is simplified and computer time is reduced.

Washington↗