Lattice BGK model for time-fractional incompressible Navier–Stokes equations

2021 ◽  
Vol 114 ◽  
pp. 106911
Author(s):  
Rui Du ◽  
Yibo Wang
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Bgk Model ◽  
Navier Stokes Equations

ON THE ASYMPTOTIC ANALYSIS OF THE BGK MODEL TOWARD THE INCOMPRESSIBLE LINEAR NAVIER–STOKES EQUATION

2010 ◽  
Vol 20 (08) ◽  
pp. 1299-1318 ◽  
Author(s):  
A. BELLOUQUID
Keyword(s):  
Asymptotic Analysis ◽  
Stokes Equations ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Uniqueness Theorems ◽  
Bgk Model ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Stokes Systems ◽  
Global Strong Solutions

This paper deals with the analysis of the asymptotic limit for BGK model to the linearized Navier–Stokes equations when the Knudsen number ε tends to zero. The uniform (in ε) existence of global strong solutions and uniqueness theorems are proved for regular initial fluctuations. As ε tends to zero, the solution of BGK model converges strongly to the solution of the linearized Navier–Stokes systems. The validity of the BGK model is critically analyzed.

A LATTICE BOLTZMANN METHOD FOR COMPUTATION OF AEROACOUSTIC INTERACTION

2007 ◽  
Vol 18 (04) ◽  
pp. 463-472 ◽  
Author(s):  
E. W. S. KAM ◽  
R. C. K. LEUNG ◽  
R. M. C. SO ◽  
X. M. LI
Keyword(s):  
Stokes Equations ◽  
Scattering Problem ◽  
Relaxation Times ◽  
Short Wave ◽  
Navier Stokes ◽  
Fluid Viscosity ◽  
Bgk Model ◽  
Navier Stokes Equations ◽  
First Case ◽  
Boltzmann Method

This paper reports a study of the ability of an improved LBM in replicating acoustic interaction. With a BGK model with two relaxation times approximating the collison term, the improved LBM is shown not only able to recover the equation of state, but also replicates the specific heat ratio, the fluid viscosity and thermal conductivity correctly. With these improvements, the recovery of full set of unsteady compressible Navier-Stokes equations is possible. Two complex aeroacoustic interaction problems, namely the interaction of three fundamental aeroacoustic pulses and scattering of short wave by a zero circulation vortex, are calculated. The LBM solutions are compared with DNS results. In the first case it has been shown that the improved LBM is as effective as the DNS in simulating aeroacoustic interaction of three pulses. Both methods obtain essentially same results using same truncated domains. In the scattering problem, LBM is able to replicate the directivity of scattered acoustic wave from the vortex but it does not accurately reproduce the symmetry as calculated using DNS.

scholarly journals A Note on the Steady Navier–Stokes Equations Derived from an ES–BGK Model for a Polyatomic Gas

Fluids ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 32
Author(s):  
Kazuo Aoki ◽  
Marzia Bisi ◽  
Maria Groppi ◽  
Shingo Kosuge
Keyword(s):  
Shock Wave ◽  
Stokes Equations ◽  
Qualitative Theory ◽  
Navier Stokes ◽  
Hydrodynamic Equations ◽  
Bgk Model ◽  
Navier Stokes Equations ◽  
Polyatomic Gas ◽  
Shock Wave Solution ◽  
Two Temperature

The two-temperature Navier–Stokes equations derived from an ellipsoidal Bhatnagar-Gross-Krook (ES-BGK) model for a polyatomic gas (Phys. Rev. E102, 023104 (2020)) are considered in regimes where bulk viscosity is much greater than the shear viscosity. Possible existence of a shock-wave solution for the steady version of these hydrodynamic equations is investigated resorting to the qualitative theory of dynamical systems. Stability properties of upstream and downstream equilibria are discussed for varying parameters.

Three-dimensional discrete-velocity BGK model for the incompressible Navier–Stokes equations

2011 ◽  
Vol 40 (1) ◽  
pp. 149-155 ◽  
Author(s):  
Akinori Tamura ◽  
Keita Okuyama ◽  
Shiro Takahashi ◽  
Masaya Ohtsuka
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Bgk Model ◽  
Navier Stokes Equations ◽  
Discrete Velocity

scholarly journals An Extension to the Navier–Stokes Equations to Incorporate Gas Molecular Collisions With Boundaries

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Erik J. Arlemark ◽  
S. Kokou Dadzie ◽  
Jason M. Reese
Keyword(s):  
Strain Rate ◽  
Stokes Equations ◽  
Fluid Dynamic ◽  
Mean Free Path ◽  
Constitutive Relationship ◽  
Navier Stokes ◽  
Molecular Collisions ◽  
Bgk Model ◽  
Stress Strain ◽  
Navier Stokes Equations

We investigate a model for microgas-flows consisting of the Navier–Stokes equations extended to include a description of molecular collisions with solid-boundaries together with first- and second-order velocity-slip boundary conditions. By considering molecular collisions affected by boundaries in gas flows, we capture some of the near-wall effects that the conventional Navier–Stokes equations with a linear stress-/strain-rate relationship are unable to describe. Our model is expressed through a geometry-dependent mean-free-path yielding a new viscosity expression, which makes the stress-/strain-rate constitutive relationship nonlinear. Test cases consisting of Couette and Poiseuille flows are solved using these extended Navier–Stokes equations and we compare the resulting velocity profiles with conventional Navier–Stokes solutions and those from the BGK kinetic model. The Poiseuille mass flow rate results are compared with results from the BGK-model and experimental data for various degrees of rarefaction. We assess the range of applicability of our model and show that it can extend the applicability of conventional fluid dynamic techniques into the early continuum-transition regime. We also discuss the limitations of our model due to its various physical assumptions and we outline ideas for further development.

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

Sign in / Sign up

Export Citation Format

Share Document