In this work, we are concerned with the lattice Boltzmann method for anisotropic convection–diffusion equations (CDEs). We prove that the collision matrices of many widely used lattice Boltzmann models for such equations admit an elegant property, which guarantees the second-order accuracy of the half-way anti-bounce-back scheme. Numerical experiments validated our results for both two- and three-dimensional anisotropic CDEs.

中文翻译：

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关于各向异性对流扩散方程的格子玻尔兹曼方法的碰撞矩阵

在这项工作中，我们关注各向异性对流扩散方程（CDE）的格子Boltzmann方法。我们证明了许多广泛用于此类方程式的格子Boltzmann模型的碰撞矩阵都具有优雅的性能，从而保证了中途防反弹回方案的二阶精度。数值实验验证了我们对二维和三维各向异性CDE的结果。