Solution of Two-Dimensional Solute Transport Model for Heterogeneous Porous Medium Using Fractional Reduced Differential Transform Method

IF 1.9 3区数学 Q1 MATHEMATICS, APPLIED

Axioms Pub Date : 2023-11-08 DOI:10.3390/axioms12111039

Manan A. Maisuria, Priti V. Tandel, Trushitkumar Patel

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Abstract

This study contains a two-dimensional mathematical model of solute transport in a river with temporally and spatially dependent flow, explicitly focusing on pulse-type input point sources with a fractional approach. This model is analyzed by assuming an initial concentration function as a declining exponential function in both the longitudinal and transverse directions. The governing equation is a time-fractional two-dimensional advection–dispersion equation with a variable form of dispersion coefficients, velocities, decay constant of the first order, production rate coefficient for the solute at the zero-order level, and retardation factor. The solution of the present problem is obtained by the fractional reduced differential transform method (FRDTM). The analysis of the initial retardation factor has been carried out via plots. Also, the influence of initial longitudinal and transverse dispersion coefficients and velocities has been examined by graphical analysis. The impact of fractional parameters on pollution levels is also analyzed numerically and graphically. The study of convergence for the FRDTM technique has been conducted to assess its efficacy and accuracy.

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非均质多孔介质二维溶质输运模型的分数阶简化微分变换解法

本研究包含一个溶质在河流中运移的二维数学模型，该模型具有时间和空间依赖的流量，明确地关注脉冲型输入点源的分数方法。通过假设初始浓度函数在纵向和横向上都是下降的指数函数来分析该模型。控制方程是一个时间分数的二维平流色散方程，具有可变形式的色散系数、速度、一阶衰减常数、溶质在零阶水平的生成速率系数和延迟因子。利用分数阶降阶微分变换方法(FRDTM)得到了该问题的解。通过绘图对初始延迟因子进行了分析。此外，还通过图形分析考察了初始纵向和横向色散系数和速度的影响。数值和图形分析了分数参数对污染水平的影响。对FRDTM技术的收敛性进行了研究，以评估其有效性和准确性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Axioms Mathematics-Algebra and Number Theory

自引率

10.00%

发文量

604

审稿时长

11 weeks

期刊介绍： Axiomatic theories in physics and in mathematics (for example, axiomatic theory of thermodynamics, and also either the axiomatic classical set theory or the axiomatic fuzzy set theory) Axiomatization, axiomatic methods, theorems, mathematical proofs Algebraic structures, field theory, group theory, topology, vector spaces Mathematical analysis Mathematical physics Mathematical logic, and non-classical logics, such as fuzzy logic, modal logic, non-monotonic logic. etc. Classical and fuzzy set theories Number theory Systems theory Classical measures, fuzzy measures, representation theory, and probability theory Graph theory Information theory Entropy Symmetry Differential equations and dynamical systems Relativity and quantum theories Mathematical chemistry Automata theory Mathematical problems of artificial intelligence Complex networks from a mathematical viewpoint Reasoning under uncertainty Interdisciplinary applications of mathematical theory.