Lattice-Boltzmann Model with Sub-Grid-Scale Boundary Conditions

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Abstract
A lattice-Boltzmann method has been developed to incorporate solid-fluid boundary conditions on length scales less than the grid spacing. By introducing a continuous parameter, specified at each node and representing the fluid volume fraction associated with that node, we obtain second-order accuracy for boundaries at arbitrary positions and orientations with respect to the grid. The method does not require surface normals, and can therefore be applied to irregular geometries such as porous media. The new rules conserve mass and momentum, and reduce to the link bounce-back rule at aligned interfaces.