scholarly journals New lattice Boltzmann model for the compressible Navier‐Stokes equations

2019 ◽  
Vol 91 (4) ◽  
pp. 183-197
Author(s):  
Takeshi Kataoka ◽  
Takaya Hanada
Keyword(s):  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Lattice Boltzmann Model ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Boltzmann Model

scholarly journals Simulating Turbulent Buoyant Flow by a Simple LES-Based Thermal Lattice Boltzmann Model

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Sheng Chen
Keyword(s):  
Lattice Boltzmann ◽  
Present Model ◽  
Stokes Equations ◽  
Lattice Boltzmann Model ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Buoyant Flow ◽  
Eddy Simulation ◽  
Thermal Lattice Boltzmann ◽  
Boltzmann Model

To simulate turbulent buoyant flow in geophysical science, where usually the vorticity-streamfunction equations instead of the primitive-variables Navier-Stokes equations serve as the governing equations, a novel and simple thermal lattice Boltzmann model is proposed based on large eddy simulation (LES). Thanks to its intrinsic features, the present model is efficient and simple for thermal turbulence simulation. Two-dimensional numerical simulations of natural convection in a square cavity were performed at high Rayleigh number varying from 104 to 1010 with Prandtl number at 0.7. The advantages of the present model are validated by numerical experiments.

Lattice Boltzmann Model for Incompressible Axisymmetric Thermal Flows With Swirl

2018 ◽  
Author(s):  
Insaf Mehrez ◽  
Ramla Gheith ◽  
Fethi Aloui ◽  
Samia Ben Nasrallah
Keyword(s):  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Thermal Conditions ◽  
Analytic Solutions ◽  
Lattice Boltzmann Model ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Wall Boundary Conditions ◽  
Physical Phenomena ◽  
Thermal Flows

This paper presents a Lattice Boltzmann (LB) model for incompressible axisymmetric thermal flows. The forces and source terms are added into the Lattice Boltzmann Equation (LBE) and the incompressible Navier-Stokes equations are recovered by the Chapman-Enskog expansion. The model of Zhou [1] is applied for axial, radial and azimuthal velocities and the model of Q.Li et al [2] is computed for temperature variation. The source term of the scheme is simple and without velocity gradient terms. This approach can solve problems including several physical phenomena and complicated force forms as the flow between two coaxial cylinders. Good agreement is obtained between the present work, the analytic solutions and results of previous studies in cylindrical pipe. It proves the efficiency and simplicity of the proposed model compared to other ones. The Taylor-Couette (TC) system is treated with water flow characterized by a radius ratio η = 0.5 and an aspect ratio Γ = 3.8. Three Reynolds numbers of 85, 100 and 150 are tested. The influence of the end-wall boundary conditions and the influence of thermal conditions on the flow structure and on the temperature distribution along the inner and outer cylinders are analyzed.

A Hybrid Lattice Boltzmann Flux Solver for Simulation of Viscous Compressible Flows

2016 ◽  
Vol 8 (6) ◽  
pp. 887-910 ◽  
Author(s):  
L. M. Yang ◽  
C. Shu ◽  
J. Wu
Keyword(s):  
Lattice Boltzmann ◽  
Compressible Flows ◽  
Stokes Equations ◽  
Strong Shock ◽  
Viscous Flows ◽  
Lattice Boltzmann Model ◽  
Navier Stokes ◽  
Inviscid Flows ◽  
Navier Stokes Equations ◽  
Viscous Compressible Flows

AbstractIn this paper, a hybrid lattice Boltzmann flux solver (LBFS) is proposed for simulation of viscous compressible flows. In the solver, the finite volume method is applied to solve the Navier-Stokes equations. Different from conventional Navier-Stokes solvers, in this work, the inviscid flux across the cell interface is evaluated by local reconstruction of solution using one-dimensional lattice Boltzmann model, while the viscous flux is still approximated by conventional smooth function approximation. The present work overcomes the two major drawbacks of existing LBFS [28–31], which is used for simulation of inviscid flows. The first one is its ability to simulate viscous flows by including evaluation of viscous flux. The second one is its ability to effectively capture both strong shock waves and thin boundary layers through introduction of a switch function for evaluation of inviscid flux, which takes a value close to zero in the boundary layer and one around the strong shock wave. Numerical experiments demonstrate that the present solver can accurately and effectively simulate hypersonic viscous flows.

scholarly journals Involving the Navier–Stokes equations in the derivation of boundary conditions for the lattice Boltzmann method

2011 ◽  
Vol 369 (1944) ◽  
pp. 2184-2192 ◽  
Author(s):  
Joris C. G. Verschaeve
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Grid Spacing ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Boltzmann Method

By means of the continuity equation of the incompressible Navier–Stokes equations, additional physical arguments for the derivation of a formulation of the no-slip boundary condition for the lattice Boltzmann method for straight walls at rest are obtained. This leads to a boundary condition that is second-order accurate with respect to the grid spacing and conserves mass. In addition, the boundary condition is stable for relaxation frequencies close to two.

DEVELOPING LBM-BASED FLUX SOLVER AND ITS APPLICATIONS IN MULTI-DIMENSION SIMULATIONS

2012 ◽  
Vol 19 ◽  
pp. 90-99
Author(s):  
KUN QU ◽  
CHANG SHU ◽  
JINSHENG CAI
Keyword(s):  
Boltzmann Equation ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Lattice Boltzmann Model ◽  
Navier Stokes ◽  
Lattice Boltzmann Equation ◽  
One Dimensional ◽  
Volume Method ◽  
Boltzmann Method ◽  
Boltzmann Model

In this paper, a new flux solver was developed based on a lattice Boltzmann model. Different from solving discrete velocity Boltzmann equation and lattice Boltzmann equation, Euler/Navier-Stokes (NS) equations were solved in this approach, and the flux at the interface was evaluated with a compressible lattice Boltzmann model. This method combined lattice Boltzmann method with finite volume method to solve Euler/NS equations. The proposed approach was validated by some simulations of one-dimensional and multi-dimensional problems.

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