Is it possible to consider a lattice Boltzmann scheme as an approximation of a partial differential equation? For a nonhomogeneous advection problem in one spatial dimension, we propose equivalent partial differential equations at various orders. We compare the lattice Boltzmann results and a spectral approximation of the differential equations. No simple correlation is obtained for a stationary problem. For an unsteady situation, we show that the initialization scheme of the microscopic moments plays a crucial role.

翻译：能否将格子玻尔兹曼格式视为偏微分方程的逼近？针对一维空间中的非齐次平流问题，我们在不同阶数下提出了等价的偏微分方程。我们将格子玻尔兹曼结果与微分方程的谱逼近进行了比较。对于稳态问题，未获得简单的相关性。针对非稳态情形，我们表明微观矩的初始化格式起着关键作用。