Qin Shenglei, Hou Guoxiang, Yang Liuming, Liu Xu, Luo Haoze
School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China.
Green & Smart River-Sea-Going Ship, Cruise and Yacht Research Center, Wuhan University of Technology, Wuhan 430063, China.
Phys Rev E. 2023 Oct;108(4-2):045305. doi: 10.1103/PhysRevE.108.045305.
In recent years, the simplified lattice Boltzmann method without evolution of distribution functions was developed, which adopts predictor-corrector steps to solve the constructed macroscopic equations. To directly solve the constructed macroscopic equations in a single step, we propose the present one-step simplified lattice Boltzmann method and apply it to simulate thermal flows under the Boussinesq approximation. The present method is derived by reconstructing the evolution equation of the lattice Boltzmann method and constructing nonequilibrium distribution functions. This method inherits the advantages of the simplified lattice Boltzmann method, such as low virtual memory cost, convenient boundary treatment, and good numerical stability at relaxation time close to 0.5. In addition, compared to the traditional artificial compressible method (ACM), the present method is more efficient in computation when a small time step is applied in the ACM to ensure numerical stability. Several numerical examples, including natural convection in a square cavity, the porous plate problem, and natural convection in a concentric annulus, are conducted to test the accuracy of the present method. The results show that this method can accurately simulate thermal flow problems and has good numerical stability.
近年来，发展了一种不涉及分布函数演化的简化格子玻尔兹曼方法，该方法采用预测 - 校正步骤来求解构建的宏观方程。为了一步直接求解构建的宏观方程，我们提出了当前的一步简化格子玻尔兹曼方法，并将其应用于模拟布辛涅斯克近似下的热流。该方法通过重构格子玻尔兹曼方法的演化方程并构建非平衡分布函数推导得出。此方法继承了简化格子玻尔兹曼方法的优点，如低虚拟内存成本、方便的边界处理以及在弛豫时间接近0.5时良好的数值稳定性。此外，与传统的人工可压缩方法（ACM）相比，当在ACM中应用小时间步长以确保数值稳定性时，本方法在计算上更高效。进行了几个数值例子，包括方腔内的自然对流、多孔板问题以及同心环内的自然对流，以测试本方法的准确性。结果表明，该方法能够准确模拟热流问题并具有良好的数值稳定性。
