https://doi.org/10.1140/epjs/s11734-024-01209-z
Regular Article
An advanced algorithm for solving incompressible fluid dynamics: from Navier–Stokes to Poisson equations
1
Zayed University, Abu Dhabi, UAE
2
Kuban State Agrarian University, Krasnodar, Russia
Received:
30
April
2024
Accepted:
14
June
2024
Published online:
25
June
2024
In this study, an extensive exploration of numerical methods for tackling the complexities of unsteady incompressible flow dynamics is undertaken. The investigation encompasses a range of cutting-edge techniques, including the Euler wavelets collocation method, nonlinear finite element method (FEM), linear FEM, and FEM with a projection step, all meticulously applied to the Navier–Stokes equation. The primary objective is to achieve an unprecedented level of accuracy in capturing fluid behavior, validated against existing numerical algorithms. The results of simulations reveal remarkable fidelity, particularly with the Euler wavelets collocation method, showcasing its exceptional capability to depict intricate velocity components and pressure fields. The nonlinear FEM technique is adept at unraveling phenomena such as bathtub vortex formation, while linear FEM and FEM with a projection step excel in capturing flow patterns around obstacles. Intriguingly, the study delves into blowup solutions, where the Euler wavelets collocation method shines brightest, predicting velocity components amidst transient phenomena with unparalleled precision. Ultimately, the study underscores the indispensable role of numerical methods in understanding the nuances of fluid dynamics, each method offering unique insights into the intricate dance of incompressible flows.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
