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Abstract: In this paper, we propose a new boundary treatment with almost second-order accuracy that does not require neighboring lattice information. In order to achieve improved accuracy for the boundary lattices, we used adaptive relaxation times reflecting boundary length scales that were unequal to the length scale of the internal fluid region lattices. Since the boundary treatment using adaptive relaxation times at the boundaries was formulated without information about the neighboring lattices, it could be easily applied to complex geometries. Numerical results using the proposed boundary treatment showed almost second-order accuracy for two-dimensional and three-dimensional problems without using information from neighboring lattices, unlike interpolation or extrapolation methods. [Copyright &y& Elsevier]