A PLATFORM FOR DEVELOPING NEW LATTICE BOLTZMANN MODELS

2005 ◽  
Vol 16 (01) ◽  
pp. 61-84 ◽  
Author(s):  
H. W. ZHENG ◽  
C. SHU ◽  
Y. T. CHEW ◽  
J. QIU
Keyword(s):  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Cavity Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Driven Cavity ◽  
Velocity Models ◽  
Equilibrium Function ◽  
New Models ◽  
Lattice Boltzmann Models

This paper presents a platform to develop new lattice Boltzmann models. It gives a general framework for different applications. It also presents basic velocity models and a set of basic conditions to construct new models which can recover Navier–Stokes equations. Besides, the equilibrium function can be easily obtained through a set of equations. By using the platform, we can easily recover the existing models. Some new models are derived from the platform and validated by their application to simulate the two-dimensional driven cavity flow. The obtained numerical results agree very well with available data in the literature.

scholarly journals Numerical Simulation of Slip effect on Lid-Driven Cavity Flow Problem for High Reynolds Number: Vorticity – Stream Function Approach

2021 ◽  
Vol 8 (3) ◽  
pp. 418-424
Author(s):  
Syed Fazuruddin ◽  
Seelam Sreekanth ◽  
G. Sankara Sekhar Raju
Keyword(s):  
Reynolds Number ◽  
Stream Function ◽  
Stokes Equations ◽  
Cavity Flow ◽  
Partial Slip ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Driven Cavity ◽  
Slip Conditions ◽  
Driven Cavity Flow

Incompressible 2-D Navier-stokes equations for various values of Reynolds number with and without partial slip conditions are studied numerically. The Lid-Driven cavity (LDC) with uniform driven lid problem is employed with vorticity - Stream function (VSF) approach. The uniform mesh grid is used in finite difference approximation for solving the governing Navier-stokes equations and developed MATLAB code. The numerical method is validated with benchmark results. The present work is focused on the analysis of lid driven cavity flow of incompressible fluid with partial slip conditions (imposed on side walls of the cavity). The fluid flow patterns are studied with wide range of Reynolds number and slip parameters.

scholarly journals NUMERICAL SIMULATION OF LID-DRIVEN CAVITY FLOW BY ISOGEOMETRIC ANALYSIS

2021 ◽  
Vol 61 (SI) ◽  
pp. 33-48
Author(s):  
Bohumír Bastl ◽  
Marek Brandner ◽  
Jiří Egermaier ◽  
Hana Horníková ◽  
Kristýna Michálková ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Incompressible Fluid ◽  
Isogeometric Analysis ◽  
Stokes Equations ◽  
Cavity Flow ◽  
Navier Stokes ◽  
Incompressible Fluid Flow ◽  
Navier Stokes Equations ◽  
Flow Solver ◽  
Driven Cavity

In this paper, we present numerical results obtained by an in-house incompressible fluid flow solver based on isogeometric analysis (IgA) for the standard benchmark problem for incompressible fluid flow simulation – lid-driven cavity flow. The steady Navier-Stokes equations are solved in their velocity-pressure formulation and we consider only inf-sup stable pairs of B-spline discretization spaces. The main aim of the paper is to compare the results from our IgA-based flow solver with the results obtained by a standard package based on finite element method with respect to degrees of freedom and stability of the solution. Further, the effectiveness of the recently introduced rIgA method for the steady Navier-Stokes equations is studied.The authors dedicate the paper to Professor K. Kozel on the occasion of his 80th birthday.

scholarly journals Lid-driven cavity flow using dual reciprocity

2020 ◽  
Vol 313 ◽  
pp. 00043
Author(s):  
Juraj Mužík ◽  
Roman Bulko
Keyword(s):  
Flow Problem ◽  
Stokes Equations ◽  
Cavity Flow ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Navier Stokes ◽  
Homogeneous Part ◽  
Navier Stokes Equations ◽  
Driven Cavity ◽  
2D Flow

The paper presents the use of the multi-domain dual reciprocity method of fundamental solutions (MD-MFSDR) for the analysis of the laminar viscous flow problem described by Navier-Stokes equations. A homogeneous part of the solution is solved using the method of fundamental solutions with the 2D Stokes fundamental solution Stokeslet. The dual reciprocity approach has been chosen because it is ideal for the treatment of the non-homogeneous and nonlinear terms of Navier-Stokes equations. The presented DR-MFS approach to the solution of the 2D flow problem is demonstrated on a standard benchmark problem - lid-driven cavity.

Lattice Boltzmann Models for Microflows

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Continuum Mechanics ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Problems ◽  
The Past ◽  
Developed Turbulence ◽  
Lattice Boltzmann Models ◽  
Boltzmann Method

The Lattice Boltzmann method was originally devised as a computational alternative for the simulation of macroscopic flows, as described by the Navier–Stokes equations of continuum mechanics. In many respects, this still is the main place where it belongs today. Yet, in the past decade, LB has made proof of a largely unanticipated versatility across a broad spectrum of scales, from fully developed turbulence, to microfluidics, all the way down to nanoscale flows. Even though no systematic analogue of the Chapman–Enskog asymptotics is available in this beyond-hydro region (no guarantee), the fact remains that, with due extensions of the basic scheme, the LB has proven capable of providing several valuable insights into the physics of flows at micro- and nano-scales. This does not mean that LBE can solve the actual Boltzmann equation or replace Molecular Dynamics, but simply that it can provide useful insights into some flow problems which cannot be described within the realm of the Navier–Stokes equations of continuum mechanics. This Chapter provides a cursory view of this fast-growing front of modern LB research.

Laminar Incompressible Recirculating Flow in a Driven Cavity of Polar Cross Section

1977 ◽  
Vol 99 (4) ◽  
pp. 774-777 ◽  
Author(s):  
U. Ghia ◽  
R. K. Goyal
Keyword(s):  
Stream Function ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Cavity Flow ◽  
Rectangular Cavity ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Driven Cavity ◽  
Recirculating Flow ◽  
Alternating Direction

The driven flow in a polar cavity has been analyzed using the complete Navier-Stokes equations formulated in terms of a stream function and vorticity. An alternating-direction implicit method, with careful treatment of the convective terms in the equations, is used to obtain the numerical solutions. Results are obtained for the stream function, vorticity, velocities and pressure for various values of the two characteristic parameters of the problem, namely, the flow Reynolds number Re and the aspect ratio of the cavity. The formulation is general and produces results for the driven rectangular cavity-flow problem as a special case. Good agreement is obtained between the present solutions for this case and available corresponding results. The overall features of the driven polar-cavity flow are found to be generally similar to those for the rectangular cavity.

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