PGD METHOD FOR PASSIVE SCALAR TRANSPORT IN A VISCOUS FLUID
Keywords:
PGD (proper generalized decomposition), separation of variables, pollutant transport and dissolution equations, numerical analysis, MatlabDOI:
https://doi.org/10.17654/0975045225014Abstract
This paper aims to study in depth the two-dimensional transport equation of a pollutant in water. We therefore proceeded to a theoretical resolution of the equation, based on a semigroup theory. Finally, a numerical resolution was obtained by the PGD (proper generalized decomposition) method. Indeed, for multidimensional models, the use of mesh discretization fails due to the exponential increase in the number of degrees of freedom associated with a multidimensional mesh or grid, requiring alternative discretization strategies. Separate representations, used in the so-called PGD (proper generalized decomposition) method, constitute an effective alternative, as demonstrated by several works. The effectiveness of the method is demonstrated by the choice of an experimental solution verifying the boundary conditions. Indeed, PGD is much faster than standard solvers, with convergence being reached after a maximum of a few enrichments.
Received: February 15, 2025
Revised: April 18, 2025
Accepted: April 28, 2025
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