Sub-zonal models for the diffusion equation with multi-material mixed cells

We describe a numerical method for the diffusion equation based upon homogenising or averaging multi-material mixed cell values. The method is computationally less expensive, than a more general method based on treating pure and mixed cells alike, but accuracy is lost in the mixed cells. In this paper we consider different sub-zonal model improvements based upon reconstruction using local based information. We present results for one and two dimensional problems, and from them conclusions are drawn to their accuracy and applicability.