在地下水污染中的对流-扩散模型的解决方案
Jalil Rashidinia1, Arefeh Momeni2, Mahboubeh Molavi-Arabshahi2
1Iran University of Science and Technology, School of Mathematics and Computer Science, Tehran, 16846-13114, Iran. rashidinia@iust.ac.ir.
Scientific reports
|January 24, 2024
概括
这项研究引入了一种高效的光谱调配方法,使用正交的伯努利多项式来解决地下水污染问题. 这种新的方法为时间分数对流-扩散模型提供了计算节约和快速融合.
科学领域:
- 数字分析 数字分析
- 环境工程环境工程
- 应用数学 应用数学 应用数学
背景情况:
- 地下水污染是一个重大的环境问题.
- 时间分数对流-扩散方程模型复杂的污染物运输.
- 现有的数值方法可能是计算密集的.
研究的目的:
- 开发一种光谱聚合方法,用于解决时间分数对流-扩散方程.
- 使用正交的伯努利多项式创建分数和经典导数的运算矩阵.
- 为了提高地下水污染模型的计算效率和准确性.
主要方法:
- 发展直角化的伯努利多项式.
- 为衍生品构建稀疏运算矩阵.
- 频谱聚合方法应用于时间微分的对流-扩散问题.
主要成果:
- 实现了具有唯一非零项的稀疏运算矩阵.
- 证明了低计算成本和快速融合.
- 通过两个测试问题验证了方法的有效性和准确性.
结论:
- 拟议的光谱聚合方法对于地下水污染的建模是准确和高效的.
- 伯努利多项式的直角化带来了计算上的优势.
- 与现有技术相比,该方法显示出更高的性能.
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