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The immersed boundary lattice Boltzmann method (IB-LBM) has been widely usedin the simulation of fluid-solid interaction and particulate flow problems,since proposed in 2004. However, it is usually a non-trivial task to retain theflexibility and the accuracy simultaneously in the implementation of thisapproach. Based on the intrinsic nature of the LBM, we propose a simple andsecond-order accurate IB-LBM in this paper, where the no-slip boundarycondition on the fluid-solid interface is directly imposed by iterativelycorrecting the distribution function near the boundary, markedly similar to thetreatment of boundary condition in the original LBM. Therefore, there are noadditional efforts needed to construct an interfacial force model (such as thespring, feedback and direct force models) and absorb this force into theframework of LBM. It is worth mentioning that we retain the discrete deltafunction for the connection between the Lagrangian and Eulerian meshes, thuspreserving the flexibility of the conventional IB-LBM. Second-order accuracy ofthe present IB-LBM is reasonably confirmed in the simulation of cylindricalCouette flow, while the conventional approach is generally a first-orderscheme. The present method is first validated in the flow past a fixedcylinder. No streamline penetration is found, indicating the exactlyenforcement of the no-slip boundary condition. Furthermore, in the simulationsof one and two particles settling under gravity, good agreements can beobserved comparing with the data available in the literature.

A distribution function correction-based immersed boundary- lattice Boltzmann method with truly second-order accuracy for fluid-solid flows