Boundary conditions for the lattice Boltzmann method in the case of viscous mixing flows

• Published in: Computers & fluids Vol. 73; pp. 145 - 161
• Main Authors: Stobiac, V., Tanguy, P.A., Bertrand, F.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 15.03.2013
• Subjects: Accuracy; Anchor impeller; Boundary conditions; Computer simulation; Extrapolation; Fluid flow; Fluids; Lattice Boltzmann method; Lattices; Paravisc impeller; Power consumption; Strategy; Viscous mixing; Boundary conditions; Anchor impeller; Power consumption; Lattice Boltzmann method; Paravisc impeller; Viscous mixing
• ISSN: 0045-7930; 1879-0747
• DOI: 10.1016/j.compfluid.2012.12.011

► We simulate viscous mixing flows with LBM and three boundary condition strategies. ► Only the extrapolation method is capable of preserving second-order accuracy. ► The immersed boundary method results in a loss of parallel efficiency. ► The modified bounce back rule is a good compromise for viscous mixing flows. This paper examines the performance of different boundary condition strategies for the lattice Boltzmann simulation of industrial viscous mixing flows. Three different strategies were chosen from the most popular approaches, which are the staircase approaches (bounce-back rules), the extrapolation or interpolation methods, and the immersed boundary methods. First, the order of convergence of the selected methods to impose boundary conditions is verified on the 3D Couette flow. This work clearly shows that only the extrapolation method is capable of preserving the second order accuracy of the lattice Boltzmann method. Second, a highly parallel LBM scheme is used to simulate fluid flow with close-clearance mixing systems in the Lagrangian frame of reference. The convergence rates obtained with the different boundary condition strategies are compared on the basis of two characteristic mixing numbers, the power number and the pumping rate. The results agree well with experimental data and finite element simulation results, and surprisingly enough, the modified bounce back rule provides a reliable accuracy despite its simplicity. Finally, the impact of the boundary condition strategies on the workload balance and the memory usage is analyzed. It appears that only the immersed boundary condition strategy modifies the parallel efficiency of the lattice Boltzmann method, yet no significant effect is observed on the memory usage.