Lattice Boltzmann models are briefly introduced together with references to methods used to predict their ability for simulations of systems described by partial differential equations that are first order in time and low order in space derivatives. Several previous works have been devoted to analyzing the accuracy of these models with special emphasis on deviations from pure Newtonian viscous behaviour, related to higher order space derivatives of even order. The presentcontribution concentrates on possible inaccuracies of the advection behaviour linked to space derivatives of odd order. Detailed properties of advection-diffusion and athermal fluids are presented for two-dimensional situations allowing to propose situations that are accurate to third order in space derivatives. Simulations of the advection of a gaussian dot or vortex are presented. Similar results are discussed in appendices for three-dimensional advection-diffusion.

翻译：本文简要介绍了格子玻尔兹曼模型，并引述了用于评估其模拟能力的方法，这些模拟系统由时间一阶、空间导数低阶的偏微分方程描述。已有若干前期工作致力于分析此类模型的精度，尤其侧重于其与纯牛顿粘性行为的偏差，这些偏差与偶数阶高阶空间导数相关。本研究的重点在于平流行为可能存在的误差，这些误差与奇数阶空间导数相关。文中详细阐述了二维情况下平流-扩散及无热流体的性质，从而提出了在空间导数上精确至三阶的模拟情形。研究展示了高斯点或涡旋平流的模拟结果。附录中讨论了三维平流-扩散的类似结果。