In the thesis, a lattice Boltzmann boundary treatment for pressure and velocity boundary conditions is presented. A new boundary condition is proposed to handle the unknown distribution functions at the boundaries. We assume every unknown distribution function has a correction term F for modification. The singular corner point is treated by two types of methods, and obtain a close result.
This scheme is applied to two-dimensional Poiseuille flow, Couette flow with wall injection, lid-driven square cavity flow, and three-dimensional Poiseuille flow. Numerical simulations exhibit the scheme is second order accurate in space discretization.

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