Lattice Boltzmann model for compressible flows on standard lattices: Variable Prandtl number and adiabatic exponent

2019 ◽  
Vol 99 (1) ◽  
Author(s):  
Mohammad Hossein Saadat ◽  
Fabian Bösch ◽  
Ilya V. Karlin
Keyword(s):  
Prandtl Number ◽  
Lattice Boltzmann ◽  
Compressible Flows ◽  
Lattice Boltzmann Model ◽  
Adiabatic Exponent ◽  
Variable Prandtl Number ◽  
Boltzmann Model

scholarly journals Lattice Boltzmann model for weakly compressible flows

2020 ◽  
Vol 101 (1) ◽  
Author(s):  
Praveen Kumar Kolluru ◽  
Mohammad Atif ◽  
Manjusha Namburi ◽  
Santosh Ansumali
Keyword(s):  
Lattice Boltzmann ◽  
Compressible Flows ◽  
Lattice Boltzmann Model ◽  
Weakly Compressible ◽  
Boltzmann Model

scholarly journals Recovery of Galilean invariance in thermal lattice Boltzmann models for arbitrary Prandtl number

2014 ◽  
Vol 25 (10) ◽  
pp. 1450046 ◽  
Author(s):  
Hudong Chen ◽  
Pradeep Gopalakrishnan ◽  
Raoyang Zhang
Keyword(s):  
Prandtl Number ◽  
Lattice Boltzmann ◽  
Relaxation Times ◽  
Collision Operator ◽  
Lattice Boltzmann Model ◽  
Operator Form ◽  
Prandtl Numbers ◽  
Lattice Boltzmann Models ◽  
Thermal Lattice Boltzmann ◽  
Boltzmann Model

In this paper, we demonstrate a set of fundamental conditions required for the formulation of a thermohydrodynamic lattice Boltzmann model at an arbitrary Prandtl number. A specific collision operator form is then proposed that is in compliance with these conditions. It admits two independent relaxation times, one for viscosity and another for thermal conductivity. But more importantly, the resulting thermohydrodynamic equations based on such a collision operator form is theoretically shown to remove the well-known non-Galilean invariant artifact at nonunity Prandtl numbers in previous thermal lattice Boltzmann models with multiple relaxation times.

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.

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