Lattice Boltzmann outflow treatments: Convective conditions and others

In this work, the first objective is to provide a lattice Boltzmann outflow scheme for the convective condition ∂tu+ū∂nu=0 of the fluid velocity (Section 3.1) in an incompressible Navier–Stokes flow. Following the asymptotic analysis, the orders of consistency and accuracy of this scheme are at least one. A series of numerical tests show that this convective outflow treatment yields solutions compatible with experiments and other numerical results. With respect to other outflow conditions concerned with zero derivatives, such as the Do-nothing condition, Grad’s approximation and a modified extrapolation method, a comparison is numerically carried out into the aspects of the condition’s influence on the interior of the flow, the mass balance, the perturbation and the reflection at the outflow. Based on the results, the convective condition of the fluid velocity demonstrates comparatively good features and is thus recommended.