This paper proposes a novel matrix assembly method called dummy scalar triplet to construct the implicit lattice Boltzmann flux solver (LBFS). The implicit discretize scheme enables the LBFS to use a time step far exceeding the Courant-Friedrichs-Lewy condition limit. Therefore, the computational efficiency and the applicability of LBFS are significantly enhanced, especially in solving complex geometry problems. In addition, a projection-based interpolation scheme is introduced to calculate the flux across the cell interface. Compared with the conventional interpolation scheme, the projection-based scheme has a higher accuracy, and its stability is hardly affected by the streaming time step. Three simulations on isotropic and anisotropic convection-diffusion equations are conducted to validate the improved method, and all the results obtained are in good agreement with the analytical solutions.

中文翻译：

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针对对流扩散方程采用基于投影的插值方案的隐式格子玻尔兹曼通量求解器

本文提出了一种称为虚拟标量三元组的新型矩阵组装方法来构造隐式格子玻尔兹曼通量求解器（LBFS）。隐式离散方案使 LBFS 能够使用远远超过 Courant-Friedrichs-Lewy 条件限制的时间步长。因此，LBFS的计算效率和适用性显着增强，特别是在解决复杂几何问题时。此外，还引入了基于投影的插值方案来计算穿过单元界面的通量。与传统的插值方案相比，基于投影的插值方案具有更高的精度，并且其稳定性几乎不受流时间步长的影响。对各向同性和各向异性对流扩散方程进行了三次模拟验证了改进方法，所得结果与解析解吻合良好。