Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/75020
Title: A particle distribution function approach to the equations of continuum mechanics in Cartesian, cylindrical and spherical coordinates : Newtonian and non-Newtonian fluids
Authors: Huilgol, RR
Kefayati, GHR 
Keywords: BGK approximation
Continuum mechanics
Lattice Boltzmann equation
Particle distribution function
Issue Date: 2018
Publisher: Elsevier B.V.
Source: Journal of non-Newtonian fluid mechanics, 2018, v. 251, p. 119-131 How to cite?
Journal: Journal of non-Newtonian fluid mechanics 
Abstract: The evolution equations for the particle distribution functions are written in a divergence form applicable in three dimensions. From this set, it is shown that the continuity equation and the equations of motion are satisfied in Cartesian, cylindrical and spherical coordinates for all fluids when additional source terms are added to the equations of evolution in the latter two coordinate systems. If the body forces are present, a new set of source functions is required in each coordinate system and these are described as well. Next, the energy equation is derived by using a separate set of particle distribution functions. Modifications of the relevant equations to be applicable to incompressible fluids is described. The incorporation of boundary conditions and the description of the numerical scheme for the simulation of the flows employing the new approach is given. Validation results obtained through the modelling of a mixed convection flow of a Bingham fluid in a lid-driven square cavity, and the steady flow of a Bingham fluid in a pipe of square cross-section are presented. Next, using the cylindrical coordinate version of the evolution equations, numerical modelling of the steady flow of a Bingham fluid and the Herschel–Bulkley fluid in a pipe of circular cross-section have been performed and compared with the simulation results using the augmented Lagrangian method as well as the analytical solutions for the velocity field and the flow rate. Finally, some comments on the theoretical differences between the present approach and the existing formulations regarding Lattice Boltzmann Equations are offered.
URI: http://hdl.handle.net/10397/75020
ISSN: 0377-0257
EISSN: 1873-2631
DOI: 10.1016/j.jnnfm.2017.10.004
Appears in Collections:Journal/Magazine Article

Access
View full-text via PolyU eLinks SFX Query
Show full item record

SCOPUSTM   
Citations

10
Last Week
0
Last month
Citations as of Oct 19, 2018

WEB OF SCIENCETM
Citations

5
Last Week
0
Last month
Citations as of Oct 20, 2018

Page view(s)

7
Last Week
0
Last month
Citations as of Oct 14, 2018

Google ScholarTM

Check

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.