格点流体力学中的迷向离散Laplacian算子
Isotropic discrete Laplacian operators from lattice hydrodynamics
摘要：
我们表明，离散计划开发的晶格流体动力学提供了一个优雅的和物理上透明的方式来推导拉普拉斯算子与各向同性离散化误差。当拉普拉斯权重遵循离散麦克斯韦-玻尔兹曼平衡时，保证各向同性，因为这些在晶格上是各向同性的。我们还指出，在三维空间中使用少至15个点，生成各向同性拉普拉斯算子。这些计算效率高的拉普拉斯算子可以用于细胞动力学和混合格子玻尔兹曼模拟，有利于流行的各向异性拉普拉斯算子，它利用更大的stentamps。该方法可以扩展到提供更高阶的离散化和其他微分算子，如梯度，散度和旋度。
英文摘要：
We show that discrete schemes developed for lattice hydrodynamics provide an elegant and physically transparent way of deriving Laplacians with isotropic discretisation error. Isotropy is guaranteed whenever the Laplacian weights follow from the discrete Maxwell-Boltzmann equilibrium since these are, by construction, isotropic on the lattice. We also point out that stencils using as few as 15 points in three dimensions, generate isotropic Laplacians. These computationally efficient Laplacians can be used in cell-dynamical and hybrid lattice Boltzmann simulations, in favor of popular anisotropic Laplacians, which make use of larger stencils. The method can be extended to provide discretisations of higher order and for other differential operators, such the gradient, divergence and curl.
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