基于改进FV-LBM的多孔介质渗流模拟

提出了一种新的基于Brimman -Forchheimer方程的多孔介质流动格子Boltzmann法的有限体积形式（FV-LBM）。在该方法中，多孔介质效应通过将外力引入格子Boltzmann方程中，并通过以单元为中心的有限体积法求解，同时将权重的校正因子引入进来以提高数值计算的稳定性。用该方法验证了完全多孔Poiseuille流和Couette流，数值计算结果与理论解吻合较好。而且还用该方法模拟了具有均匀和非均匀孔隙度的裂隙-孔隙模型，结果表明：当达西数增加时，多孔层中的速度增加；而当裂隙区域的速度峰值减小时，速度轮廓接近抛物线。研究成果为多孔介质渗流模拟提供了有效途径。

Simulation of hydrodynamics in porous media using improved finite volume-lattice Boltzmann method

Fluid flow through porous media is of great importance for many natural systems, such as groundwater flow transport, pollution diffusion and geothermal exploitation. In this paper, a novel finite volume formulation of the lattice Boltzmann method for porous media flows was proposed based on the Brinkman–Forchheimer equation. In this method, the porous media effect was introduced into the lattice Boltzmann equation by external force, and solved by finite volume method centered on the element, and the correction factor of the weight was introduced to improve the numerical calculation stability. The fully porous Poiseuille flow and Couette flow was verified by this method, and the numerical results were in good agreement with the theoretical solution. Finally, the fracture-pore model with uniform and non-uniform porosity was simulated by this method. The results showed that the velocity in the porous layer increased when the number of Daisy increased. While the velocity peak in the fracture region decreased and the velocity profile approached the parabola. This method provides an effective way for porous media seepage simulation.