论文标题
一致的晶格Boltzmann方法，用于卷平均Navier-Stokes方程
Consistent lattice Boltzmann methods for the volume averaged Navier-Stokes equations
论文作者
论文摘要
我们得出了一种新型的晶格玻尔兹曼方案，该方案使用压力校正强迫项来近似于最多三个维度的体积平均Navier-Stokes方程（VANSE）。通过对晶格玻尔兹曼方程的零矩的新定义，考虑到空间和时间上不同的局部体积分数。 Chapman-Enskog分析尊重本地体积的变化，正式证明了VanSe限制到高阶项的一致性。通过稳态和非平稳示例对方案的数值验证批准相对于速度和压力的二阶收敛。此处提出的晶格玻尔兹曼方法是第一个使用二阶恢复压力的时空变化的体积分数。
We derive a novel lattice Boltzmann scheme, which uses a pressure correction forcing term for approximating the volume averaged Navier-Stokes equations (VANSE) in up to three dimensions. With a new definition of the zeroth moment of the Lattice Boltzmann equation, spatially and temporally varying local volume fractions are taken into account. A Chapman-Enskog analysis, respecting the variations in local volume, formally proves the consistency towards the VANSE limit up to higher order terms. The numerical validation of the scheme via steady state and non-stationary examples approves the second order convergence with respect to velocity and pressure. The here proposed lattice Boltzmann method is the first to correctly recover the pressure with second order for space-time varying volume fractions.
