A dimensionless numerical mesh-free model for the compressible fluid flows. (15th May 2021)

• Record Type: Journal Article
• Authors: Rammane, Mohammed; Mesmoudi, Said; Tri, Abdeljalil; Braikat, Bouazza; Damil, Noureddine
• Is Part Of: Computers & fluids. Volume 221(2021)
• Publication Date: 2021-05-15
• Subjects: Compressible fluid flow -- Navier-Stokes equations -- Meshless method -- Moving least squares -- Implicit Euler -- Homotopy technique -- Taylor series expansion -- Continuation technique; Fluid dynamics -- Data processing -- Periodicals; 532.050285
• DOI: 10.1016/j.compfluid.2021.104845
• Languages: English
• ISSNs: 0045-7930

Abstract

Highlights: We propose a dimensionless numerical mesh-free model. The formulation os the Navier-Stokes equations is a dimensionless form. The performance of the presented model is tested on the standard benchmark lid-driven cavity problem. Abstract: In this paper, we propose a dimensionless numerical mesh-free model for the simulation of the compressible isothermal viscous flows. The novelty of this work consists to formulate the Navier-Stokes equations under a dimensionless form and to solve them by a high order mesh-free algorithm to simulate the compressible fluid flows. This algorithm combines a classical implicit Euler scheme, a high order continuation with the Moving Least Squares (MLS) and a homotopy transformation. The MLS approximation and implicit Euler scheme are used respectively for the spatial and temporal discretizations of dimensionless Navier-Stokes equations. The homotopy transformation serves to introduce in dimensionless Navier Stokes equations an arbitrary operator and a parameter without physical dimension. The obtained equations are solved by a high order continuation. The performance of the presented model is tested on the standard benchmark lid-driven cavity problem. Then, the Mach and Reynolds numbers effect is discussed. The obtained results are compared with those of the Finite Difference Method (FDM) coupled with an explicit Runge-Kutta (R-K) scheme and those of literature. This comparison reveals that the results of the dimensionless model are obtained with a less expensive CPU time compared to that of the other algorithms.