arXiv subjects

Xiao-Jun Gu

Publications and source records attributed to Xiao-Jun Gu.

5 recordsLinked to original sources

arXiv2023

Impact of reconstruction schemes on interpreting lattice Boltzmann results -- A study using the Taylor-Green vortex problem

In this note, we show how reconstruction schemes can have a significant impact on interpreting lattice Boltzmann simulation data. To reconstruct turbulence quantities, e.g., the kinetic energy dissipation rate and enstrophy, schemes higher than second-order for spatial derivatives can greatly improve the prediction of these quantities in the Taylor-Green vortex problem. In contrast, a second-order reconstruction of the time series data indicates very good accuracy for the kinetic energy dissipation rate. The present findings can be considered as further numerical evidence of the capability of the lattice Boltzmann method to simulate turbulent flows, which is consistent with its proven feature of low numerical diffusion.

physics.flu-dyn↗

arXiv2018

On the relationship between the diffuse reflection and bounce-back boundary condition in the continuum limit

In this work, we show that the widely used bounce-back boundary condition is an incomplete form of the diffuse reflection boundary condition at the continuum limit for lattice Boltzmann simulations. By utilizing this fact, we can force the diffuse reflection scheme to work at its continuum limit so that the no-slip boundary condition can be implemented without any non-physical slip velocity error being induced by the standard bounce-back scheme. The revised boundary formulation is validated numerically by solving a pressure-driven channel flow, a lid-driven cavity flow and channel flow around a square cylinder.

physics.flu-dyn↗

arXiv2018

Discrete Boltzmann model of shallow water equations with polynomial equilibria

A type of discrete Boltzmann model for simulating shallow water flows is derived by using the Hermite expansion approach. Through analytical analysis, we study the impact of truncating distribution function and discretizing particle velocity space. It is found that the convergence behavior of expansion is nontrivial while the conservation laws are naturally satisfied. Moreover, the balance of source terms and flux terms for steady solutions is not sacrificed. Further numerical validations show that the capability of simulating supercritical flows is enhanced by employing higher order expansion and quadrature.

physics.flu-dyn↗

arXiv2017

A comment on `An improved macroscale model for gas slip flow in porous media'

In a recent paper by Lasseux, Valdés-Parada and Porter (J.~Fluid~Mech. \textbf{805} (2016) 118-146), it is found that the apparent gas permeability of the porous media is a nonlinear function of the Knudsen number. However, this result is highly questionable, because the adopted Navier-Stokes equations and the first-order velocity-slip boundary condition are first-order (in terms of the Knudsen number) approximations of the Boltzmann equation and the kinetic boundary condition for rarefied gas flows. Our numerical simulations based on the Bhatnagar-Gross-Krook kinetic equation and regularized 20-moment equations prove that the Navier-Stokes equations with the first-order velocity-slip boundary condition are only accurate at a very small Knudsen number limit, where the apparent gas permeability is a linear function of the Knudsen number.

physics.flu-dyn↗

arXiv2015

Slip velocity of lattice Boltzmann simulation using bounce-back boundary scheme

In this work we investigate the issue of non-physical slip at wall of lattice Boltzmann simulations with the bounce-back boundary scheme. By comparing the analytical solution of two lattice models with four and nine discrete velocities for the force-driven Poiseuille flow, we are able to reveal the exact mechanism causing the issue. In fact, no boundary condition is defined by the bounce-back scheme for the the discrete velocities parallel to wall. Other factors, such as initial conditions and inlet and outlet boundary conditions, can play the role and induce the non-physical slip velocity. Therefore, the issue is not related to the single-relaxation-time scheme. Naturally the key for resolving it is to specify the definition for these velocities. Through a lid-driven cavity flow, we show that the solution can be as easy as no extra effort required for simple geometries, although further study is necessary for complex geometries.

physics.flu-dyn↗