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Analytical solutions to a nonlinear diffusion–advection equation
| Content Provider | Semantic Scholar |
|---|---|
| Author | Pudasaini, Shiva P. Hajra, Sayonita Ghosh Kandel, Santosh Khattri, Khim B. |
| Copyright Year | 2018 |
| Abstract | In this paper, we construct some exact and analytical solutions to a nonlinear diffusion and advection model (Pudasaini in Eng Geol 202: 62–73, 2016) using the Lie symmetry, travelling wave, generalized separation of variables, and boundary layer methods. The model in consideration can be viewed as an extension of viscous Burgers equation, but it describes significantly different physical phenomenon. The nonlinearity in the model is associated with the quadratic diffusion and advection fluxes which are described by the sub-diffusive and sub-advective fluid flow in general porous media and debris material. We also observe that different methods consistently produce similar analytical solutions. This highlights the intrinsic characteristics of the flow of fluid in porous material. The nonlinear diffusion and advection is characterized by a gradually thinning tail that stretches to the rear of the fluid and the evolution of forward advecting frontal bore head, in contrast to the classical linear diffusion and advection. Additionally, we compare solutions for the linear and nonlinear diffusion and advection models highlighting the similarities and differences. The analytical solutions constructed in this paper and the existing high-resolution numerical solution presented previously for the nonlinear diffusion and advection model independently support each other. This implies that the exact and analytical solutions constructed here are physically meaningful and can potentially be applied to calculate the complex nonlinear re-distribution of fluid in porous landscape, and debris and porous materials. |
| Starting Page | 1 |
| Ending Page | 20 |
| Page Count | 20 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s00033-018-1042-6 |
| Volume Number | 69 |
| Alternate Webpage(s) | http://www2.geo.uni-bonn.de/members/pudasaini/Pudasaini_Papers/Pudasaini_etal_2018.pdf |
| Alternate Webpage(s) | https://doi.org/10.1007/s00033-018-1042-6 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
