An efficient boundary condition-implemented immersed boundary-lattice Boltzmann method for simulation of 3D incompressible viscous flows

• No-slip boundary condition is accurately implemented as compared to previous works.
• First order Dirac delta function interpolation used in conventional IB-LBM is avoided.
• Second order Lagrange interpolation is used to implement boundary condition.
• Calculation of forces on the immersed boundary is simple and easy.
• It can easily simulate complex 3D flows and no flow penetration is found.

An efficient boundary condition-implemented immersed boundary-lattice Boltzmann method (IB-LBM) is presented in this paper. In this work, no-slip boundary condition is directly used to modify velocities at boundary-dependent points through the second-order Lagrange interpolation. As a consequence, flow penetration is avoided and more accurate results are acquired. The boundary-dependent points can be easily identified from intersection points between Cartesian mesh lines and the immersed boundary. Another important contribution of this work is to use Newton’s second law to compute forcing terms at the boundary-dependent points. Due to presence of the solid boundary, velocity change between pre-modified velocity and post-modified velocity will generate acceleration. This acceleration can be used to compute force given from the boundary. Numerical experiments show that present solver has the second-order of overall accuracy. To validate the present method, three-dimensional (3D) incompressible viscous flow over a sphere is first simulated. Then simulations of complicated 3D moving boundary flows are conducted. Numerical results show that the flow penetration of conventional IB-LBM is completely eliminated, and the results obtained agree very well with available data in the literature.