Due to the potential for significant cost-savings, many companies are turning their attention to digital simulations to improve their products and develop new ones. Although software is available to support these efforts, there is a growing need in industry to improve the accuracy of predictions from these codes. The goal of this project is to conduct research required for the development of a new prototype software package for engineering simulations in continuum mechanics (e.g., fluid flows, heat transfer, electromagnetics, etc.) based on an innovative concept known as “cut-stencils”.