Bibliographic Details
| Title: |
A new mathematical model for traveling sand dunes: analysis and approximation. |
| Authors: |
Falcone, M.1 (AUTHOR) falcone@mat.uniroma1.it, Finzi Vita, S.1 (AUTHOR) finzi@mat.uniroma1.it |
| Source: |
Applied Numerical Mathematics. Sep2020, Vol. 155, p208-225. 18p. |
| Subjects: |
Mathematical models, Finite differences, Sand dunes, Erosion |
| Abstract: |
We present a new two-layer closed form model for the dynamics of desert dunes under the effect of a horizontal wind blowing in an arbitrary direction. This model is an extension of a very simplified model previously introduced by Hadeler and Kuttler [12]. Our extension, inspired by the sandpile dynamics approach, includes the effects of gravity on both sides (upwind and downwind) of the dune, and allows to describe erosion and deposition in a more accurate way. After a discussion of the model and its properties we present a numerical scheme based on finite differences in 1D and we prove its consistency and stability. Some numerical tests show a good qualitative behavior and a realistic shape for the evolving dunes. Finally, we discuss the preliminary steps of a possible extension of this model to the 2D case. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
