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Mass conservation and momentum transfer across solid-fluid boundaries have been active topics through the development of the lattice-Boltzmann method. In this paper, we review typical treatments to prevent net mass transfer across solid-fluid boundaries in the lattice-Boltzmann method, and argue that such efforts are in general not necessary and could lead to incorrect results. Carefully designed simulations are conducted to examine the effects of normal boundary movement, tangential density gradient, and lattice grid resolution. Our simulation results show that the global mass conservation can be well satisfied even with local unbalanced mass transfer at boundary nodes, while a local mass conservation constraint can produce incorrect flow and pressure fields. These simulations suggest that local mass conservation, at either a fluid or solid boundary node, is not only an unnecessary consequence to maintain the global mass conservation, but also harmful for meaningful simulation results. In addition, the concern on the momentum addition and reduction associated with status-changing nodes is also not technically necessary. Although including this momentum addition or reduction has no direct influence on flow and pressure fields, the incorrect fluid-particle interaction may affect simulation results of particulate suspensions.

A dynamic stiffness method is presented for the vibrations of plate structures that are reinforced by eccentric stiffeners. The model incorporates both out-of-plane and in-plane deformations of the plates and the stiffeners. Based on the relationship between the forces and displacements along the common edges of the plate or beam elements, the dynamic stiffness formulae for the plate and the beam elements are derived, respectively. The globally assembled dynamic stiffness matrix is then obtained using the finite element method so that the dynamics of built-up stiffened plates can be readily addressed by using the present method. Compared to the conventional finite element model, the dynamic stiffness model can provide very accurate solutions using only one element over each uniform plate and beam member, regardless of its geometry.