Abstract
To determine the origin of the numerical instability and energy dissipation caused by the spurious current in existing numerical wave tanks (NWTs), a detailed theoretical analysis is presented of the free-surface boundary treatment in the lattice Boltzmann (LB) method (LBM). The force imbalance-induced error, which is generated by the inconsistency between gravity and the pressure gradient and by the second-order moment of the forcing term, is proved to be the cause of the spurious current. To solve the instability and dissipation problem, a modified LB scheme that introduces gravity into the pressure gradient is proposed to ensure force balance, and an improved NWT using the LBM is developed based on this modified scheme. Numerical experiments show that the improved NWT exhibits good performance in simulating progressive waves and nonlinear wave transformations without spurious current and energy dissipation problems.
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