A lattice-Boltzmann method has recently been developed to incorporate solid-fluid boundary conditions on length scales less than the grid spacing. By introducing a real numbered parameter, specified at each node and representing the fluid volume associated with that node, we were able to accurately simulate arbitrary geometries without the need to specify surface normals. In this paper a detailed description of the rules is presented and the accuracy and stability of the method is discussed, based on numerical results for flow in systems with planar surfaces and for flow through periodic arrays of disks and spheres.