scholarly journals Discrete Velocity Boltzmann Model for Quasi-Incompressible Hydrodynamics

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 993
Author(s):  
Oleg Ilyin
Keyword(s):  
Cross Sections ◽  
Lattice Boltzmann ◽  
Present Model ◽  
Test Problems ◽  
Hydrodynamic Equations ◽  
Interacting Particles ◽  
Closed Expression ◽  
Discrete Velocity ◽  
H Theorem ◽  
Boltzmann Model

In this paper, we consider the development of the two-dimensional discrete velocity Boltzmann model on a nine-velocity lattice. Compared to the conventional lattice Boltzmann approach for the present model, the collision rules for the interacting particles are formulated explicitly. The collisions are tailored in such a way that mass, momentum and energy are conserved and the H-theorem is fulfilled. By applying the Chapman–Enskog expansion, we show that the model recovers quasi-incompressible hydrodynamic equations for small Mach number limit and we derive the closed expression for the viscosity, depending on the collision cross-sections. In addition, the numerical implementation of the model with the on-lattice streaming and local collision step is proposed. As test problems, the shear wave decay and Taylor–Green vortex are considered, and a comparison of the numerical simulations with the analytical solutions is presented.

Numerical Simulations on Hydrodynamic Process of Melt Jet Breakup and Fragmentation With the Two-Phase Lattice Boltzmann Method

2018 ◽  
Author(s):  
Shimpei Saito ◽  
Yutaka Abe ◽  
Akiko Kaneko ◽  
Alessandro De Rosis ◽  
Alessio Festuccia ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Lattice Boltzmann ◽  
Present Model ◽  
Three Dimensional ◽  
Lattice Boltzmann Model ◽  
Hydrodynamic Process ◽  
Two Phase ◽  
Jet Breakup ◽  
Boltzmann Method ◽  
Boltzmann Model

Jet breakup and fragmentation are important phenomena to be well understood during a core-disruptive accident of sodium-cooled fast reactors. The three-dimensional two-phase lattice Boltzmann model developed previously by the authors is improved in numerical stability used to simulate the hydrodynamic process of melt jet breakup. Nonorthogonal central moments is successfully introduced into the model. Numerical simulations of FARO-TERMOS experiments demonstrate the enhancements in stability of the present model. The simulations with two types of grid resolutions show the effect of spatial resolution on the results.

LATTICE BOLTZMANN MODEL FOR SIMULATING VISCOUS COMPRESSIBLE FLOWS

2010 ◽  
Vol 21 (03) ◽  
pp. 383-407 ◽  
Author(s):  
Y. WANG ◽  
Y. L. HE ◽  
Q. LI ◽  
G. H. TANG ◽  
W. Q. TAO
Keyword(s):  
Distribution Function ◽  
Kernel Function ◽  
Lattice Boltzmann ◽  
Compressible Flows ◽  
Present Model ◽  
Mach Reflection ◽  
Lattice Boltzmann Model ◽  
Polynomial Kernel ◽  
Viscous Compressible Flows ◽  
Boltzmann Model

A lattice Boltzmann model is developed for viscous compressible flows with flexible specific-heat ratio and Prandtl number. Unlike the Maxwellian distribution function or circle function used in the existing lattice Boltzmann models, a polynomial kernel function in the phase space is introduced to recover the Navier–Stokes–Fourier equations. A discrete equilibrium density distribution function and a discrete equilibrium total energy distribution function are obtained from the discretization of the polynomial kernel function with Lagrangian interpolation. The equilibrium distribution functions are then coupled via the equation of state. In this framework, a model for viscous compressible flows is proposed. Several numerical tests from subsonic to supersonic flows, including the Sod shock tube, the double Mach reflection and the thermal Couette flow, are simulated to validate the present model. In particular, the discrete Boltzmann equation with the Bhatnagar–Gross–Krook approximation is solved by the finite-difference method. Numerical results agree well with the exact or analytic solutions. The present model has potential application in the study of complex fluid systems such as thermal compressible flows.

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.

INCOMPRESSIBLE MRT LATTICE BOLTZMANN MODEL WITH EIGHT VELOCITIES IN 2D SPACE

2009 ◽  
Vol 20 (07) ◽  
pp. 1023-1037 ◽  
Author(s):  
RUI DU ◽  
BAOCHANG SHI
Keyword(s):  
Relaxation Time ◽  
Lattice Boltzmann ◽  
Present Model ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Lattice Boltzmann Model ◽  
Time Model ◽  
Single Relaxation Time ◽  
Double Shear ◽  
Boltzmann Model

In this paper a two-dimensional-eight-velocity lattice Boltzmann model with multi-relaxation-time is proposed for incompressible flows, in which the equilibria in the momentum space are derived from an earlier incompressible lattice Boltzmann model with single relaxation time. Through the Chapman–Enskog expansion, the incompressible Navier–Stokes equations can be recovered. Numerical tests, including the steady Poiseuille flow, the double shear flow and the driven cavity flow, have been carried out to verify the present model. The numerical results agree well with the analytical solutions or the existing results, and it is found that the present model exhibits much better numerical stability than the single relaxation time model.

A Hermite-based lattice Boltzmann model with artificial viscosity for compressible viscous flows

2018 ◽  
Vol 32 (13) ◽  
pp. 1850157 ◽  
Author(s):  
Ruofan Qiu ◽  
Rongqian Chen ◽  
Chenxiang Zhu ◽  
Yancheng You
Keyword(s):  
Distribution Function ◽  
Lattice Boltzmann ◽  
Viscous Flows ◽  
Artificial Viscosity ◽  
Lattice Boltzmann Model ◽  
Hermite Expansion ◽  
Discrete Velocity ◽  
Velocity Models ◽  
Compressible Viscous Flows ◽  
Boltzmann Model

A lattice Boltzmann model on Hermite basis for compressible viscous flows is presented in this paper. The model is developed in the framework of double-distribution-function approach, which has adjustable specific-heat ratio and Prandtl number. It contains a density distribution function for the flow field and a total energy distribution function for the temperature field. The equilibrium distribution function is determined by Hermite expansion, and the D3Q27 and D3Q39 three-dimensional (3D) discrete velocity models are used, in which the discrete velocity model can be replaced easily. Moreover, an artificial viscosity is introduced to enhance the model for capturing shock waves. The model is tested through several cases of compressible flows, including 3D supersonic viscous flows with boundary layer. The effect of artificial viscosity is estimated. Besides, D3Q27 and D3Q39 models are further compared in the present platform.

Development and Comparative Studies of Three Non-free Parameter Lattice Boltzmann Models for Simulation of Compressible Flows

2012 ◽  
Vol 4 (04) ◽  
pp. 454-472 ◽  
Author(s):  
L. M. Yang ◽  
C. Shu ◽  
J. Wu
Keyword(s):  
Lattice Boltzmann ◽  
Free Parameter ◽  
Compressible Flows ◽  
Computation Time ◽  
Distribution Functions ◽  
Lattice Boltzmann Model ◽  
Test Problems ◽  
One Dimensional ◽  
Application Range ◽  
Boltzmann Model

AbstractThis paper at first shows the details of finite volume-based lattice Boltzmann method (FV-LBM) for simulation of compressible flows with shock waves. In the FV-LBM, the normal convective flux at the interface of a cell is evaluated by using one-dimensional compressible lattice Boltzmann model, while the tangential flux is calculated using the same way as used in the conventional Euler solvers. The paper then presents a platform to construct one-dimensional compressible lattice Boltzmann model for its use in FV-LBM. The platform is formed from the conservation forms of moments. Under the platform, both the equilibrium distribution functions and lattice velocities can be determined, and therefore, non-free parameter model can be developed. The paper particularly presents three typical non-free parameter models, D1Q3, D1Q4 and D1Q5. The performances of these three models for simulation of compressible flows are investigated by a brief analysis and their application to solve some one-dimensional and two-dimensional test problems. Numerical results showed that D1Q3 model costs the least computation time and D1Q4 and D1Q5 models have the wider application range of Mach number. From the results, it seems that D1Q4 model could be the best choice for the FV-LBM simulation of hypersonic flows.

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