对于地下水污染的三维多项分数异常溶液运输模型的解决方案
Imtiaz Ahmad1, Ihteram Ali2, Rashid Jan3
1Institute of Informatics and Computing in Energy (IICE), Universiti Tenaga Nasional, Kajang, Selangor, Malaysia.
PloS one
|December 8, 2023
概括
本研究介绍了一种无网格计算方法,用于模拟复杂的扩散方程. 这种新的方法为地下水污染等问题提供了准确和高效的解决方案.
科学领域:
- 计算数学 计算数学 计算数学
- 数字分析 数字分析
- 科学计算科学计算
背景情况:
- 分数扩散方程模型复杂的运输现象.
- 时间分数移动-不移动扩散方程在污染物运输等领域至关重要.
- 现有的数值方法在更高的维度中实施可能是复杂的.
研究的目的:
- 开发和验证一个无网格计算方法,用于3D多期时间分数移动-不移动扩散方程.
- 为了证明这种复杂问题的无网格方法的简单性和效率.
- 为地下水污染和类似领域的应用提供强大的数值工具.
主要方法:
- 一个稳定的Crank-Nicolson时间整合方案与时间离散的Caputo衍生定义相结合.
- 对空间导数近似使用了反向多方体辐射基函数.
- 无网格方法将问题分离到分散或均的节点上,产生稀疏的矩阵.
主要成果:
- 拟议的无网格方法准确地模拟了3D多项时间分数移动-不移动扩散方程.
- 在各种域形状上的数值模拟验证了该方法与分析解决方案的准确性.
- 这种方法在实施中表现出了简单性,特别是对于更高的维度.
结论:
- 无网格技术为解决复杂的分数扩散问题提供了强大而高效的替代方案.
- 开发的方法显示了实际应用的巨大潜力,包括地下水污染建模.
- 这项研究证实了无网格方法在实施方便和准确性方面的优势.
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