A multi-entropy-level lattice Boltzmann model for the one-dimensional compressible Euler equations

Abstract

In this paper, we propose a new lattice Boltzmann model for the one-dimensional compressible Euler equations. The new model is based on a three-entropy-level and three-speed lattice Boltzmann equation by using a method of higher-order moments of the equilibrium distribution functions. In order to obtain the second-order accuracy model, we employ the ghost field distribution functions to remove the non-physical dissipation terms in the Euler equations. We also use the conditions of the higher-order moments of the ghost field equilibrium distribution functions to obtain the equilibrium distribution functions. The numerical examples show that the numerical results can be compared with those classical methods.

Influences of pH and CO2 on the formation of Metasilicate mineral water in Changbai Mountain, Northeast China

“…Using Boltzmann reaction kinetic model (Yan and Zhang 2008;Liu and Zhou 2009) to simulate the release process of metasilicate of the carbonated solution experiment (initial pH neutral and alkaline), cumulative release was estimated by Eq. 3.…”

A lattice Boltzmann model for two‐dimensional sound wave in the small perturbation compressible flows

“…We assume that f ln( f /w ) can be expressed as linear form of f S . The numerical values S A , S B , and S D can be determined by the stability of lattice Boltzmann scheme [34], and also can be selected as the numerical values in the energy-level model [32].…”

“…Because the equation for wave cannot reflect the information about all the physical quantities, such as density, pressure, velocity of flows, etc., the properties for sound wave but not for wave in another form may be lost, such as the conservation of entropy in the gas flows. On the other hand, the strategy selected is not to simulate the compressible Navier-Stokes equations and compressible Euler equations directly by employing the previous LBM for compressible flows [31][32][33][34]. The reasons are that compressible lattice Boltzmann models are more complicated, and are not for the small perturbation variables.…”

“…The reasons are that compressible lattice Boltzmann models are more complicated, and are not for the small perturbation variables. For example, the moment is 0 i j = u i u j + p i j in compressible LBM [31][32][33][34], but it is 0 i j =p i j in this small perturbation model. Thus, we no more need to build a model as complicated as that for the full Navier-Stokes equations.…”

14-velocity and 18-velocity multiple-relaxation-time lattice Boltzmann models for three-dimensional incompressible flows

“…The earliest LBGK model is proposed by Qian et al [10], which is often used to simulate the incompressible flow in the low Mach number limit. However, through the Chapman- [11,12], while in our paper we are focused on how to reduce the compressible effect in existing LB models.…”