Boundary slip from the immersed boundary lattice Boltzmann models

Abstract

We report an interesting and important observation of the velocity fields from immersed boundary lattice Boltzmann methods (IB-LBM). The computed velocity profiles can deviate from theoretical predictions greatly even for very simple flow situations, both in the immersed boundary layer and the bulk region. A rigorous analysis of the IB-LBM simulated velocity for a symmetric shear flow is carried out, and the analytical solutions indicate a strong dependence of velocity on the relaxation parameter (kinetic viscosity). Also our simulations demonstrate that simply increasing the immersed boundary layer thickness is not an efficient approach to reduce such velocity discrepancy. We hope this work will bring the awareness of this essential issue to people using IB-LBM for various flow situations.

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“…To obtain the analytical solution of the velocity slip in the the multi-direct forcing method with 2 relaxation times, we follow the procedure of Le et al 16 and He et al 45 Because f k (x + e k t , t + t ) = f k (x, t) for k = 1 and 3 in a steady state, Equations 21a, 21b, and 47 yield …”

“…11 Although some methods succeeded in accurately enforcing the nonslip boundary condition, the numerical errors in the velocity and the velocity gradient at the boundary, which are referenced collectively as boundary slip, increase with relaxation time in numerical simulation by the IB-LBM. 16 The use of the multirelaxation time (MRT) collision operator 17 solved the problem of boundary slip occurring at high relaxation times in the IB-LBM. 18 The two-relaxation-time (TRT) collision operator 19 reduced the boundary slip velocity as effectively as the MRT collision operator.…”

“…20 Another boundary error, ie, the disagreement between the boundary velocity on the Eulerian node and the desired velocity, also increases with increasing relaxation time in the IB-LBM calculation. 16,18 By solving systems of algebraic equations, the implicit velocity-correction method with the TRT collision operator succeeded in removing all boundary errors that depend on the relaxation time. 21 Although Zhang et al numerically demonstrated that the IB-LBM using the iterative procedure with the MRT collision operator also reduced the boundary errors, they did not completely eliminate the velocity slip in their numerical calculations.…”