Lattice Boltzmann Fluid Simulation with Neumann Boundary Conditions
摘要
This chapter offers an extended investigation of the lattice Boltzmann method (LBM) for simulating thermal flows in closed cavities, with particular focus on the implementation of Neumann-type boundary conditions. We present a theoretical overview of the method, highlighting its kinetic foundations and its ability to solve efficiently the Navier–Stokes and thermal transport equations. The treatment of hydrodynamic and thermal boundary conditions is analyzed with a focus on the classical approaches and recent methodology of Neumann conditions implementation. To validate the robustness and accuracy of this new methodology, a computational study is conducted on an air-filled square cavity, exposed to constant heat fluxes imposed on the vertical sidewalls according to the Neumann scheme. The results of this simulation are discussed in terms of temperature distributions, streamlines, as well as local and global Nusselt numbers, confirming the relevance of the model implemented. This work represents a significant contribution to advanced numerical modeling of heat transfer with more realistic boundary conditions.