scholarly journals Numerical Modeling of Water Table Fluctuation in Unconfined Sloping Aquifer in Response to Multiple Localized Recharge

2021 ◽  
pp. 13-23
Author(s):  
Shikha Saxena ◽  
Rajeev Kumar Bansal ◽  
Basant Singh
Keyword(s):  
Numerical Modeling ◽  
Porous Media ◽  
Numerical Model ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Water Table ◽  
Boussinesq Equation ◽  
Water Table Fluctuation ◽  
Aquifer Parameters ◽  
Sloping Aquifer

Numerical modeling for the variations of water table fluctuation in response to subsurface seepage and downwards recharge is an important aspect in the estimation of surface-groundwater interaction. In this work, a numerical model is developed for the approximation of water table variation in an unconfined sloping aquifer subjected to the multiple localized recharge and seepage from the adjacent water body. The Boussinesq equation characterizing the flow of groundwater in unconfined sloping porous media is solved numerically using Du Fort Frankel finite difference method. The application of the result is demonstrated with illustrative examples using varying aquifer parameters. The results indicated that the water table form groundwater mound beneath recharge basins due to continuous recharge.

Numerical Modeling of a Nonlinear MEMS Membrane

2004 ◽  
Author(s):  
Owen I. Crabtree ◽  
Sinisa Dj. Mesarovic ◽  
Ismail Demir ◽  
Robert F. Richards ◽  
David F. Bahr ◽  
...  
Keyword(s):  
Residual Stress ◽  
Numerical Modeling ◽  
Numerical Model ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Empirical Data ◽  
Geometrically Nonlinear ◽  
Mems Device ◽  
The Finite Difference Method ◽  
Stress Layer

A numerical model is developed to understand the behavior of a laminated, piezoelectric, geometrically nonlinear MEMS device. The finite difference method is chosen, along with the Newmark technique to model the static and vibrational behavior. This technique is validated by comparison to empirical data. The developed model is exercised to understand and optimize the device by studying residual stress, layer thicknesses, and electrode sizes with the goal of reduction of fundamental frequency and increase of charge output.

2-D AUTOMATIC COMPOSITION OF NODAL VALUES FROM NUMERICAL MODEL USING SCRIPT PROGRAMMING

2013 ◽  
Vol 62 (1) ◽  
Author(s):  
Rudi Heriansyah
Keyword(s):  
Finite Element ◽  
Numerical Modeling ◽  
Numerical Model ◽  
Finite Difference ◽  
Two Dimensional ◽  
Commercial Software ◽  
One Dimensional ◽  
Automatic Composition ◽  
The Individual ◽  
Individual Nodes

There are many commercial software to perform numerical modeling based on finite element (FEM) and finite difference (FDM) methods. It is often a requirement to the designer, that the values of the individual nodes in the numerical model are known. Usually, these softwares provide two methods to achieve this; firstly, by clicking directly onto the nodes of interest and secondly, by saving or exporting the whole nodal values to an external file. The former way is appropriate for models with small number of nodes, but as the number of nodes increases, it is no longer an efficient or effective way. Through the latter method, all nodal values are obtained, however the values are one-dimensional, and in some cases, only certain nodal values are required for presentation. In this paper, an algorithm for automatic composition of nodal values obtained from the second method mentioned above. The composed nodal values will be in two-dimensional form as this is the format used for uniform shaped model (square or rectangular). Since numerical softwares usually have facilities to save the data in a spreadsheet format, the proposed algorithm is implemented in this environment by using spreadsheet script programming.

On: “Wave Propagation in heterogeneous, porous media: A velocity‐stress, finite difference method,” by N. Dai, A. Vafidis, and E. R. Kanasewich (March‐April 1995 GEOPHYSICS, p. 327–340).

Geophysics ◽  
1996 ◽  
Vol 61 (4) ◽  
pp. 1230-1231 ◽  
Author(s):  
Boris Gurevich
Keyword(s):  
Porous Media ◽  
Wave Propagation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Seismic Wave Propagation ◽  
Heterogeneous Porous Media ◽  
Two Dimensions ◽  
Seismic Modeling ◽  
Modeling Technology ◽  
Interesting Paper

In their interesting paper the authors present a new advanced approach to the simulation of seismic wave propagation in media described by Biot’s theory of dynamic poroelasticity in two dimensions. The algorithm developed can be used to accurately simulate the effect of dynamic poroelasticity on seismic wavefields over hydrocarbon reservoirs. In cases where this effect proves significant this algorithm can be incorporated in the seismic modeling technology.

scholarly journals A Fourth Order Finite Difference Method for the Good Boussinesq Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
M. S. Ismail ◽  
Farida Mosally
Keyword(s):  
Exact Solution ◽  
Nonlinear System ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Fourth Order ◽  
Boussinesq Equation ◽  
First Order ◽  
System A ◽  
Accuracy And Stability ◽  
Linearization Techniques

The “good” Boussinesq equation is transformed into a first order differential system. A fourth order finite difference scheme is derived for this system. The resulting scheme is analyzed for accuracy and stability. Newton’s method and linearization techniques are used to solve the resulting nonlinear system. The exact solution and the conserved quantity are used to assess the accuracy and the efficiency of the derived method. Head-on and overtaking interactions of two solitons are also considered. The numerical results reveal the good performance of the derived method.

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