International Journal of Mathematical Sciences and Computing (IJMSC)
IJMSC Vol. 8, No. 4, 8 Oct. 2022
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Mathematical Based Implicit and Explicit Finite Difference Techniques for Solving the Ground Water Flow Equations Using Spreadsheets
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Index Terms
Critical thinking, explicit, groundwater modelling, finite difference, implicit, spreadsheet
Abstract
In countries with arid and semi-arid climate such as Iran with water constraints, the use of groundwater resources is very important. There are various mathematical based methods and software packages for modelling groundwater resources. This paper uses groundwater flow problems to illustrate possible approaches for providing the environment of active teaching. Mathematical models supported by software applications facilitate the gaining of an insight into the physical behaviors by investigating a host of scenarios and events but they are poor in training critical thinking for encapsulating the hardcore mathematical equations describing the problems. Whilst software engineering has transformed the intellectual capitals accumulated between the 20th century and the middle of the 21th century into working tools, it has the drawback of encapsulating core mathematics away from common experience of the students and practitioners. This diminishes critical thinking in a world of increasing risks and ought to be taken a serious side effect of software engineering. This paper suggests a solution by building up a library of solvers using spreadsheets, with the effect that the encapsulated knowledge of building modelling solvers can permanently be brought to life in education with the active learning culture. Implementation was carried out in the same way for steady state flow as well as explicit 2D and 3D finite difference approximation for transient flow. This study raises concern about the encapsulated body of knowledge contributed to the emergence and the establishment of modelling software applications since 1980. This body of knowledge comprise a deeper understanding of equations of often partial differential equations describing physical problems, as well as their numerical transformation into systems of equations and their subsequent properly- and improperly posed systems of equation in terms of their assumptions and quality conditions. The outcome is the emergence of a cookbook mentality among the new breed of mathematical modelers without any critical thinking. The results revealed that spreadsheet can be used with the aid of the Solver function. This idea capitalized on the capabilities of the net-generation and opens up the possibility for the emergence of bottom-up open source modelling platforms.
Cite This Paper
Farzin Salmasi, Mohammad Taghi Sattari, Halit Apaydin, " Mathematical Based Implicit and Explicit Finite Difference Techniques for Solving the Ground Water Flow Equations Using Spreadsheets", International Journal of Mathematical Sciences and Computing(IJMSC), Vol.8, No.4, pp. 1-14, 2022. DOI: 10.5815/ijmsc.2022.04.01
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