A general method for the derivation of equivalent finite difference equations (EFDEs) and subsequent equivalent partial differential equations (EPDEs) is presented for a general matrix lattice Boltzmann method (LBM). The method can be used for both the advection diffusion equations and Navier–Stokes equations in all dimensions.

In principle, the EFDEs are derived using a recurrence formula. A computational algorithm is proposed for generating sequences of matrices and vectors that are used to obtain EFDEs coefficients. For all DdQq velocity models, the algorithm is proven to be finite and all coefficients are obtained after $q$ iterations. The resulting EFDEs and EPDEs are derived for selected velocity models and include the single relaxation time, multiple relaxation times, and cascaded LBM collision operators.

The algorithm for the derivation of EFDEs and EPDEs is implemented in C++ using the GiNaC library for symbolic algebraic computations. Its implementation is available under the terms and conditions of the GNU general public license (GPL).

针对通用矩阵格子玻尔兹曼方法（LBM），提出了推导等效有限差分方程（EFDE）和随后的等效偏微分方程（EPDE）的通用方法。该方法可用于所有维度的对流扩散方程和Navier–Stokes方程。

原则上，EFDE是使用递归公式得出的。提出了一种计算算法，用于生成用于获得EFDE系数的矩阵和向量序列。对于所有DdQq速度模型，该算法均证明是有限的，并且所有系数均在$q$迭代。得出的EFDE和EPDE用于选定的速度模型，包括单个弛豫时间，多个弛豫时间和级联LBM碰撞算子。

EFDE和EPDE的推导算法是使用GiNaC库在C ++中实现的，用于符号代数计算。可根据GNU通用公共许可证（GPL）的条款和条件使用其实现。