Steady-state analytical solutions for the lattice boltzmann equation

Open Physics ◽  
2003 ◽  
Vol 1 (3) ◽  
Author(s):  
Gábor Házi
Keyword(s):  
Steady State ◽  
Boltzmann Equation ◽  
Analytical Solutions ◽  
Poiseuille Flow ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Lattice Boltzmann Equation ◽  
Two Dimensional ◽  
Navier Stokes Equations

AbstractA general class of analytical solutions of the lattice Boltzmann equation is derived for two-dimensional, steady-state unidirectional flows. A subset of the solutions that verifies the corresponding Navier-Stokes equations is given. It is pointed out that this class includes, e.g., the Couette and the Poiseuille flow but not, e.g., the basic Kolmogorov flow. For steady-state non-unidirectional flows, first and second order solutions of the lattice Boltzmann equation are derived. Practical consequences of the analysis are mentioned. Differences between the technique applied here and those used in some earlier works are emphasized.

Navier-Stokes Computation of Radial Inflow Turbine Distributor

1988 ◽  
Vol 110 (1) ◽  
pp. 29-32 ◽  
Author(s):  
T. C. Vu ◽  
W. Shyy
Keyword(s):  
Experimental Data ◽  
Steady State ◽  
Energy Loss ◽  
Stokes Equations ◽  
Flow Analysis ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Two Dimensional Flow ◽  
Radial Inflow Turbine

A two-dimensional flow analysis of a radial inflow turbine distributor using full steady-state Reynolds-averaged Navier-Stokes equations is made. The numerical prediction of the total energy loss and the wicket gate torque is compared with experimental data. Also, a parametric study is carried out in order to evaluate the behavior of the numerical algorithm.

scholarly journals Hydrodynamic stability and turbulent transition with the Vreman LES SGS and a modified lattice Boltzmann equation

2018 ◽  
Author(s):  
J. R. Murdock ◽  
S. L. Yang
Keyword(s):  
Boltzmann Equation ◽  
Lattice Boltzmann ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Flow Characteristics ◽  
Transition To Turbulence ◽  
Scale Model ◽  
Navier Stokes ◽  
Lattice Boltzmann Equation ◽  
Intermittent Turbulence

For the evaluation of a broad range of Re in incompressible flows, particularly unsteady and transition regimes, the Vreman subgrid scale model is studied within the framework of a modified lattice Boltzmann equation. A unique multiple relaxation time form which recovers the fully incompressible unsteady Navier-Stokes equations is derived for the D3Q19 lattice. Solutions to the 3D-driven cavity are compared to a number of lattice Boltzmann and Navier-Stokes solutions. Initial simulations demonstrate the vanishing nature of eddy viscosity in the steady laminar regime. Onset of unsteadiness is found between Re 1900 and 1950, matching well with the wealth of literature. At Re 6000, velocity history and complex vortex structures show a transition to turbulence near the domain bottom and front walls while the centre of the domain retains laminar characteristics. By Re 8000 intermittent turbulence has progressed to the domain centre. This range of Re for transition and the flow characteristics are in agreement with the general ranges in literature, with further observations being added here. The Vreman model with an incompressible lattice Boltzmann method is found to be a promising tool for laminarto- turbulent simulation.

scholarly journals Simulation of Poiseuille flow

2021 ◽  
pp. 1-29
Author(s):  
Georgy Sergeevich Chashchin
Keyword(s):  
Lattice Boltzmann Method ◽  
Poiseuille Flow ◽  
Lattice Boltzmann ◽  
High Speed ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Cartesian Grids ◽  
Navier Stokes Equations ◽  
Advantages And Disadvantages ◽  
Boltzmann Method

In this article, plane and space Poiseuille flow was simulate of the lattice Boltzmann method. Because Poiseuille solution is one of the simplest solutions Navier-Stokes equations, it is well for exploring opportunities of lattice Boltzmann method. Simulation flows in plane rectangular and ellipsoidal cylindrical pipes assist to detect advantages and disadvantages of original and Dellar’s regularized lattice Boltzmann algorithm on standard lattices with different started and boundaries conditions. LBM’s main excellence is high speed of calculation, but it’s manifest imperfection is using Cartesian grids and not evident generalization on another grid’s types.

Internal laminar flow

2018 ◽  
Author(s):  
Marcel Escudier
Keyword(s):  
Poiseuille Flow ◽  
Stokes Equations ◽  
Circular Cross Section ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Concentric Cylinder ◽  
Navier Stokes Equations ◽  
Concentric Cylinders ◽  
Constant Viscosity ◽  
Pressure Driven Flow

In this chapter it is shown that solutions to the Navier-Stokes equations can be derived for steady, fully developed flow of a constant-viscosity Newtonian fluid through a cylindrical duct. Such a flow is known as a Poiseuille flow. For a pipe of circular cross section, the term Hagen-Poiseuille flow is used. Solutions are also derived for shear-driven flow within the annular space between two concentric cylinders or in the space between two parallel plates when there is relative tangential movement between the wetted surfaces, termed Couette flows. The concepts of wetted perimeter and hydraulic diameter are introduced. It is shown how the viscometer equations result from the concentric-cylinder solutions. The pressure-driven flow of generalised Newtonian fluids is also discussed.

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