An advanced algorithm for solving incompressible fluid dynamics: from Navier–Stokes to Poisson equations

Document Type

Article

Source of Publication

European Physical Journal: Special Topics

Publication Date

1-1-2024

Abstract

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.

ISSN

1951-6355

Publisher

Springer Science and Business Media LLC

Disciplines

Life Sciences

Keywords

Incompressible Fluid Dynamics, Navier–Stokes Equation, Numerical Methods, Euler Wavelets Collocation Method, Finite Element Method (FEM)

Scopus ID

85196858401

Indexed in Scopus

yes

Open Access

no

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