Meshless Lagrangian SPH method applied to isothermal lid-driven cavity flow at low-Re numbers

• Published in: Computational particle mechanics Vol. 5; no. 4; pp. 467 - 475
• Main Authors: Fraga Filho, C. A. D., Chacaltana, J. T. A., Pinto, W. J. N.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01-10-2018; Springer Nature B.V
• Subjects: Cavity flow; Classical and Continuum Physics; Collocation methods; Computational fluid dynamics; Computational Science and Engineering; Computer simulation; Energy conservation; Engineering; Finite element method; Fluid flow; Fluid mechanics; FORTRAN; Mathematical analysis; Mathematical models; Meshless methods; Programming languages; Theoretical and Applied Mechanics; Velocity distribution; Navier–Stokes equations; Low Reynolds numbers; Incompressible Newtonian fluid; Physical laws of conservation; SPH particle method; Lid-driven cavity
• ISSN: 2196-4378; 2196-4386
• DOI: 10.1007/s40571-018-0183-x

SPH is a recent particle method applied in the cavities study, without many results available in the literature. The lid-driven cavity flow is a classic problem of the fluid mechanics, extensively explored in the literature and presenting a considerable complexity. The aim of this paper is to present a solution from the Lagrangian viewpoint for this problem. The discretization of the continuum domain is performed using the Lagrangian particles. The physical laws of mass, momentum and energy conservation are presented by the Navier–Stokes equations. A serial numerical code, written in Fortran programming language, has been used to perform the numerical simulations. The application of the SPH and comparison with the literature (mesh methods and a meshless collocation method) have been done. The positions of the primary vortex centre and the non-dimensional velocity profiles passing through the geometric centre of the cavity have been analysed. The numerical Lagrangian results showed a good agreement when compared to the results found in the literature, specifically for
Re
<
100.00
. Suggestions for improvements in the SPH model presented are listed, in the search for better results for flows with higher Reynolds numbers.