Subgrid-scale models using anisotropic eddy-viscosity tensors are considered and used to derive new numerical schemes for Large Eddy Simulations. The derivation is based on integral representations of differential operators and directly leads to algorithms using only velocity values at grid points. The asymptotic behavior of the model near boundaries is discussed and several implementation options are described, including techniques for backscatter control which distinguish between the strain directions in the flow. A numerical validation is carried out on channel flow calculations and possible extensions of the method are outlined.