A brief review on the solutions of advection-diffusion equation

Authors

  • Pushpa Nidhi Gautam Patan Multiple Campus, Tribhuvan University, Kathmandu, Nepal
  • Buddhi Prasad Sapkota Ratna Rajyalaxmi Campus, Tribhuvan University, Kathmandu, Nepal
  • Kedar Nath Uprety Tribhuvan University, Kathmandu, Nepal

DOI:

https://doi.org/10.3126/sw.v15i15.45668

Keywords:

Cole-Hopf transformation, Integral transform, Dispersion, Viscosity

Abstract

In this work both linear and nonlinear advection-diffusion equations are considered and discussed their analytical solutions with different initial and boundary conditions. The work of Ogata and Banks, Harleman and Rumer, Cleary and Adrian, Atul Kumar et al., Mojtabi and Deville are reviewed for linear advection-diffusion equations and for nonlinear, we have chosen the work of Sakai and Kimura. Some enthusiastic functions used in the articles, drawbacks and applications of the results are discussed. Reduction of the advection-diffusion equations into diffusion equations make the governing equation solvable by using integral transform method for analytical solution. For nonlinear advection-diffusion equations, the Cole-Hopf transformation is used to reduce into the diffusion equation. Different dispersion phenomena in atmosphere, surface and subsurface area are outlined.

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Author Biography

Kedar Nath Uprety, Tribhuvan University, Kathmandu, Nepal

Central Department of Mathematics

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Published

2022-06-14

How to Cite

Gautam, P. N., Sapkota, B. P., & Uprety, K. N. (2022). A brief review on the solutions of advection-diffusion equation. Scientific World, 15(15), 4–9. https://doi.org/10.3126/sw.v15i15.45668

Issue

Section

Research Article