Folders: ROOT > ScienceBase Catalog > USGS National Research Program > USGS National Research Program Projects > Application of Stochastic Processes in Hydrogeology ( Show direct descendants )
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A two-dimensional control volume mixed finite element method is applied to the elliptic equation. Discretization of the computational domain is based in triangular elements. Shape functions and test functions are formulated on the basis of an equilateral reference triangle with unit edges. A pressure support based on the linear interpolation of elemental edge pressures is used in this formulation. Comparisons are made between results from the standard mixed finite element method and this control volume mixed finite element method. Published 2011. This article is a US Government work and is in the public domain in the USA.
Categories: Publication;
Types: Citation;
Tags: Darcy problem,
Mix,
control volume,
elliptic equation
A geometric multigrid solver (GMG), based in the preconditioned conjugate gradient algorithm, has been developed for solving systems of equations resulting from applying the cell-centered finite difference algorithm to flow in porous media. This solver has been adapted to the U.S. Geological Survey ground-water flow model MODFLOW-2000. The documentation herein is a description of the solver and the adaptation to MODFLOW-2000.
Categories: Publication;
Types: Citation
The preconditioned conjugate gradient with improved nonlinear control (PCGN) package provides addi-tional means by which the solution of nonlinear ground-water flow problems can be controlled as compared to existing solver packages for MODFLOW. Picard iteration is used to solve nonlinear ground-water flow equations by iteratively solving a linear approximation of the nonlinear equations. The linear solution is provided by means of the preconditioned conjugate gradient algorithm where preconditioning is provided by the modi-fied incomplete Cholesky algorithm. The incomplete Cholesky scheme incorporates two levels of fill, 0 and 1, in which the pivots can be modified so that the row sums of the preconditioning matrix...
Categories: Publication;
Types: Citation
Summary. In this study, an new vector test function is proposed for two-dimenional control volume mixed nite-element methods where discretization of the computational domain is based in triangular elements. The proposed test function has the advantage of allowing for a pressure-eld approximation that is piecewise smooth rather than piece- wise constant. Implementation of the test function, in association with the usual vector shape functions for triangular elements, is described. In the control-volume approach, the product of the test function and the ux approximation (obtained using associate shape functions) are integrated over a lesser volume than the full triangular element. With the proposed test function,...
Categories: Publication;
Types: Citation;
Tags: Darcy flow,
Mixe,
control volume,
mixed nite element
A geometric multigrid solver (GMG), based in the preconditioned conjugate gradient algorithm, has been developed for solving systems of equations resulting from applying the cell-centered finite difference algorithm to flow in porous media. This solver has been adapted to the U.S. Geological Survey ground-water flow model MODFLOW-2000. The documentation herein is a description of the solver and the adaptation to MODFLOW-2000.
Categories: Publication;
Types: Citation
Categories: Publication;
Types: Citation
The mixed finite-element approximation to a second-order elliptic PDE results in a saddle-point problem and leads to an indefinite linear system of equations. The mixed system of equations can be transformed into coupled symmetric positive-definite matrix equations, or a Schur complement problem, using block Gauss elimination. A preconditioned conjugate-gradient algorithm is used for solving the Schur complement problem. The mixed finite-element method is closely related to the cell-centered finite difference scheme for solving second-order elliptic problems with variable coefficients. For the cell-centered finite difference scheme, a simple multigrid algorithm can be defined and used as a preconditioner. For distorted...
Categories: Publication;
Types: Citation
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