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Formulation of Numerical Equations
Abstract The purpose of this paper is to develop the numerical equations for the Finite Difference Method (FDM), the Integral Finite Difference Method (IFDM) and the Finite Element Method (FEM). The numerical equations formulated will incorporate appropriate provisions for handling such special features as boundary conditions, initial conditions, heterogeneities, anisotropy, sources, time- or potential-dependent changes in parameters and so on. The next step is to describe the methods by which various differencing schemes can be employed to march in the time domain. The end-product of these efforts is an assemblage of conservation equations for each discrete subspace of the flow region of interest. If desired, these equations can be organized as a matrix of equations which can be solved by direct or iterative methods of solution. Numerical equations are sufficiently general in their structure to include porous or/and fractured materials. Therefore, a discussion about the manner in which either type of material can be handled in a generalized numerical formulation is of considerable interest. The objective of this study is to provide an overall conceptual-mathematical framework in which the different numerical methods can be compared and contrasted. The treatment will be restricted to isothermal fluid-flow in saturated-unsaturated deformable media. This class of problems is usually written in the form of a non-linear parabolic differential equation. It is hoped that this section will serve as a useful introduction to the next two papers.
Formulation of Numerical Equations
Abstract The purpose of this paper is to develop the numerical equations for the Finite Difference Method (FDM), the Integral Finite Difference Method (IFDM) and the Finite Element Method (FEM). The numerical equations formulated will incorporate appropriate provisions for handling such special features as boundary conditions, initial conditions, heterogeneities, anisotropy, sources, time- or potential-dependent changes in parameters and so on. The next step is to describe the methods by which various differencing schemes can be employed to march in the time domain. The end-product of these efforts is an assemblage of conservation equations for each discrete subspace of the flow region of interest. If desired, these equations can be organized as a matrix of equations which can be solved by direct or iterative methods of solution. Numerical equations are sufficiently general in their structure to include porous or/and fractured materials. Therefore, a discussion about the manner in which either type of material can be handled in a generalized numerical formulation is of considerable interest. The objective of this study is to provide an overall conceptual-mathematical framework in which the different numerical methods can be compared and contrasted. The treatment will be restricted to isothermal fluid-flow in saturated-unsaturated deformable media. This class of problems is usually written in the form of a non-linear parabolic differential equation. It is hoped that this section will serve as a useful introduction to the next two papers.
Formulation of Numerical Equations
Narasimhan, T. N. (author)
1984-01-01
32 pages
Article/Chapter (Book)
Electronic Resource
English
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