An improved off-lattice algorithm for the open boundary in the lattice Boltzmann method

Lattice Boltzmann method (LBM) becomes a popular fluid solver in recent decades due to its natural parallelization and ease of handling complex geometries. Boundary conditions in LBM need special treatments to employ macroscopic values (velocity, pressure, etc.) into discrete distribution functions on these boundary nodes. Many no-slip wall treatments already exist in this field, such as Zou/He, Bouzidi, and Guo algorithms, but the open boundary is still a field needed more study. Although many existing wall treatments can be extended to velocity boundary conditions by adding additional terms, the accuracy might be a concerning shortage, especially on the corner nodes (in 2D) or the edge nodes (in 3D). Hence, in this presentation, we will discuss an improved algorithm based on the Bouzidi algorithm with a focus on the corner/edge node treatments and extend it into the Dirichlet pressure boundary condition. Several numerical tests with different flow types will also be presented to show the better accuracy of our algorithm.