The article deals with the numerical simulations for equations of geophysical fluids. These physical phenomena are modeled by the Navier-Stokes equations which describe the motion of the fluid, the ocean currents, the flow of water in a pipe and many other fluid flow phenomenon.These equations are very useful because of there utility. The Navier-Stokes equations for incompressible flow are nonlinear partial differential equations that drive the motion of fluids in the approximation of continuous media. The existence of general solutions to the Navier Stokes equations have already proven but in this paper we have interested to the numerical solution of the incompressible Navier-Stokes equations. We get an optimal discretization of the Navier-Stokes equations and numerical approximations of the solution are also given. The convergence and the stabilityof the approximated system are proven. The numerical resolution is based on Hermite finite elements. The numerical system was expressed in matrix form for computation of velocity and the pression fieldsapproach using MATLAB software. Numerical results for velocity field in two dimensional space of the velocity u(x,y) and pression p(x,y,) are given. And finally we give physical interpretation of the results obtained.
| Published in | International Journal of Applied Mathematics and Theoretical Physics (Volume 7, Issue 4) |
| DOI | 10.11648/j.ijamtp.20210704.14 |
| Page(s) | 112-125 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Numerical Simulation, Geophysical Models, Navier-Stokes Equation, Stokes Equations, Hermite Finite Elements, Numerical Simulations
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APA Style
Ibrahima Thiam, Babou Khady Thiam, Ibrahima Faye. (2021). Numerical Simulation of Ocean Currents with Hermite IFinite Elements. International Journal of Applied Mathematics and Theoretical Physics, 7(4), 112-125. https://doi.org/10.11648/j.ijamtp.20210704.14
ACS Style
Ibrahima Thiam; Babou Khady Thiam; Ibrahima Faye. Numerical Simulation of Ocean Currents with Hermite IFinite Elements. Int. J. Appl. Math. Theor. Phys. 2021, 7(4), 112-125. doi: 10.11648/j.ijamtp.20210704.14
AMA Style
Ibrahima Thiam, Babou Khady Thiam, Ibrahima Faye. Numerical Simulation of Ocean Currents with Hermite IFinite Elements. Int J Appl Math Theor Phys. 2021;7(4):112-125. doi: 10.11648/j.ijamtp.20210704.14
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Download@article{10.11648/j.ijamtp.20210704.14,
author = {Ibrahima Thiam and Babou Khady Thiam and Ibrahima Faye},
title = {Numerical Simulation of Ocean Currents with Hermite IFinite Elements},
journal = {International Journal of Applied Mathematics and Theoretical Physics},
volume = {7},
number = {4},
pages = {112-125},
doi = {10.11648/j.ijamtp.20210704.14},
url = {https://doi.org/10.11648/j.ijamtp.20210704.14},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20210704.14},
abstract = {The article deals with the numerical simulations for equations of geophysical fluids. These physical phenomena are modeled by the Navier-Stokes equations which describe the motion of the fluid, the ocean currents, the flow of water in a pipe and many other fluid flow phenomenon.These equations are very useful because of there utility. The Navier-Stokes equations for incompressible flow are nonlinear partial differential equations that drive the motion of fluids in the approximation of continuous media. The existence of general solutions to the Navier Stokes equations have already proven but in this paper we have interested to the numerical solution of the incompressible Navier-Stokes equations. We get an optimal discretization of the Navier-Stokes equations and numerical approximations of the solution are also given. The convergence and the stabilityof the approximated system are proven. The numerical resolution is based on Hermite finite elements. The numerical system was expressed in matrix form for computation of velocity and the pression fieldsapproach using MATLAB software. Numerical results for velocity field in two dimensional space of the velocity u(x,y) and pression p(x,y,) are given. And finally we give physical interpretation of the results obtained.},
year = {2021}
}
TY - JOUR T1 - Numerical Simulation of Ocean Currents with Hermite IFinite Elements AU - Ibrahima Thiam AU - Babou Khady Thiam AU - Ibrahima Faye Y1 - 2021/12/24 PY - 2021 N1 - https://doi.org/10.11648/j.ijamtp.20210704.14 DO - 10.11648/j.ijamtp.20210704.14 T2 - International Journal of Applied Mathematics and Theoretical Physics JF - International Journal of Applied Mathematics and Theoretical Physics JO - International Journal of Applied Mathematics and Theoretical Physics SP - 112 EP - 125 PB - Science Publishing Group SN - 2575-5927 UR - https://doi.org/10.11648/j.ijamtp.20210704.14 AB - The article deals with the numerical simulations for equations of geophysical fluids. These physical phenomena are modeled by the Navier-Stokes equations which describe the motion of the fluid, the ocean currents, the flow of water in a pipe and many other fluid flow phenomenon.These equations are very useful because of there utility. The Navier-Stokes equations for incompressible flow are nonlinear partial differential equations that drive the motion of fluids in the approximation of continuous media. The existence of general solutions to the Navier Stokes equations have already proven but in this paper we have interested to the numerical solution of the incompressible Navier-Stokes equations. We get an optimal discretization of the Navier-Stokes equations and numerical approximations of the solution are also given. The convergence and the stabilityof the approximated system are proven. The numerical resolution is based on Hermite finite elements. The numerical system was expressed in matrix form for computation of velocity and the pression fieldsapproach using MATLAB software. Numerical results for velocity field in two dimensional space of the velocity u(x,y) and pression p(x,y,) are given. And finally we give physical interpretation of the results obtained. VL - 7 IS - 4 ER -
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