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<p>In our study, we tackle a linear advection-diffusion equation that varies with time and is constrained to one dimension, under the framework of homogeneous Dirichlet boundary conditions. We employ two distinct approaches for solving this equation: an analytical solution through the method of separation of variables, and a numerical solution utilizing the finite difference method. The computational output includes three dimensional (3D) plots for solutions, focusing on pollutants such as Ammonia, Carbon monoxide, Carbon dioxide, and Sulphur dioxide. Concentrations, along with their respective diffusivities, are analyzed through 3D plots and actual calculations. To comprehend the diffusivity-concentration relationship for predicting pollutant movement in the air, the domain is divided into two halves. The study explores the behavior of pollutants with higher diffusivity entering regions with lower diffusivity, and vice versa, using 2D and 3D plots. This task is crucial for effective pollution control strategies, and safeguarding the environment and public health.</p>

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On one dimensional advection-diffusion equation with variable diffusivity

  • 期刊论文

  • 发表日期：

    2026年3月1日

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  • Eeshwar Prasad Poudel,
  • Pitambar Achaya,
  • Jeevan Kafle,
  • Shreeram Khadka

摘要

In our study, we tackle a linear advection-diffusion equation that varies with time and is constrained to one dimension, under the framework of homogeneous Dirichlet boundary conditions. We employ two distinct approaches for solving this equation: an analytical solution through the method of separation of variables, and a numerical solution utilizing the finite difference method. The computational output includes three dimensional (3D) plots for solutions, focusing on pollutants such as Ammonia, Carbon monoxide, Carbon dioxide, and Sulphur dioxide. Concentrations, along with their respective diffusivities, are analyzed through 3D plots and actual calculations. To comprehend the diffusivity-concentration relationship for predicting pollutant movement in the air, the domain is divided into two halves. The study explores the behavior of pollutants with higher diffusivity entering regions with lower diffusivity, and vice versa, using 2D and 3D plots. This task is crucial for effective pollution control strategies, and safeguarding the environment and public health.