The main purpose of this paper is to develop the PGD (proper generalized decomposition), which is a model reduction method where the solution is sought under separate form to the solution of the transport and dissolution equations of pollutants in water. We test the efficiency of the method with the choice of an experimental solution which verifies edge conditions.

PGD (proper generalized decomposition), separation of variables, pollutant transport and dissolution equations, numerical analysis, Matlab.

Received: May 9, 2021; Accepted: June 10, 2021; Published: June 15, 2021

How to cite this article: Djibo Moustapha, Badjo Kimba Abdoul Wahid and Pr Saley Bisso,PGD type dimensional reduction for solving the equation of transport and dissolution of pollutants in water, Far East Journal of Applied Mathematics 110(1)(2021), 49-64. DOI: 10.17654/AM110010049

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References

[1] Francisco Chinesta, Roland Keunings and Adrien Leygue, The Proper Generalized Decomposition for Advanced Numerical Simulations, Springer Briefs in Applied Sciences and Technology, Library of Congress Control Number: 2013951633, 2014.
[2] Elias Cueto, David Gonzalez and Iciar Alfaro, Proper Generalized Decompositions An Introduction to Computer Implementation with Matlab, Springer Briefs in Applied Sciences and Technology, Library of Congress Control Number: 2016933200, 2016.
[3] Francisco Chinesta and Elias Cueto, PGD-based Modeling of Materials, Structures and Processes, ESAFORM Book Series on Material Forming, Library of Congress Control Number: 2014937278, 2014.
[4] A. Dumon, C. Allery and A. Ammar, Proper general decomposition (PGD) for the resolution of Navier-Stokes equations, J. Comput. Phys. 230 (2011), 1387-1407.
[5] David Gonzalez, Elias Cueto, Francisco Chinesta, Pedro Diez and Antonio Huerta, Streamline upwind/Petrov-Galerkin-based stabilization of proper generalized decompositions for high-dimensional advection-diffusion equations, Internat. J. Numer. Methods Engrg. 94 (2013), 1216-1232.