Diffuse reflection boundary condition for high-order lattice Boltzmann models with streaming–collision mechanism

For lattice Boltzmann (LB) models, their particle feature is ensured by the streaming–collision mechanism. However, this mechanism is often discarded for high-order LB models due to multi-speed lattices. Here, we propose a new way of implementing the diffuse reflection boundary condition that can maintain the characteristic streaming–collision mechanism for high-order models. It is then tested on four lattice models, namely D2Q16, D2Q17, D2Q37 and D3Q121 for isothermal and thermal Couette flows and lid-driven cavity flows. Our implementation is shown to be able to achieve second-order accuracy globally.