An exact non-equilibrium extrapolation scheme for pressure and velocity boundary conditions with large gradients in the lattice Boltzmann method

In this work, an exact non-equilibrium extrapolation (eNEQ) scheme for velocity and pressure boundary conditions in the lattice Boltzmann method is proposed. Based on the non-equilibrium extrapolation (NEQ) scheme, well designed parameters are introduced to correct the distribution functions. Numerical results of velocity and pressure driven Poiseuille flows demonstrate that the present eNEQ scheme is of second-order spatial accuracy for both velocity and pressure boundary conditions. In addition, a series of other numerical simulation results show that in some cases with the large pressure or velocity gradient at the boundary, the eNEQ scheme can well ensure the accuracy of the calculation results, while the NEQ scheme performs struggle due to the adoption of the extrapolation scheme. On the basis of retaining the advantages of the original NEQ scheme, the present eNEQ scheme can be used to implement the velocity and pressure boundary conditions exactly.