A flexible forcing three dimension IB–LBM scheme for flow past stationary and moving spheres

• A novel flexible forcing IB–LBM scheme is introduced for 3D problems.
• Flexible forcing/sub-iteration is utilised to satisfy the no-slip condition.
• Complex matrix calculation is avoided using a convergence scheme.
• Stationary and moving boundary 3D problems are simulated.
• Experimental verification is also provided.

The recently proposed (Dash et al., 2013) flexible forcing immersed boundary (IB)–lattice Boltzmann method (LBM) is improved in this work to simulate three dimensional fluid–solid interaction problems. In conventional IB–LBM schemes, explicit calculation of the force density may produce unsatisfactory no-slip boundary condition. This further leads to unphysical streamline penetrations and improper force/torque calculations for the stationary/moving spheres. Following an implicit calculation of the force density, a single Lagrangian velocity correction term is prescribed here to satisfy the no-slip condition within a convergence limit. This formulation is mathematically simple and with the help of flexible number of sub-iteration/forcing, the computational time is significantly reduced. The proposed new version of IB–LBM model is validated with three-dimension flow past stationary and moving spheres, and the results are found in excellent agreement with the data obtained from in-house experiments and previous literatures.