This paper presents Large Eddy Simulation (LES) as a unified framework that weaves together its three core components: filtering, modeling and discretization. The method begins by removing small‑scale motions through the application of the conservation laws over control volumes of user‑specified size, thereby defining the computational grid. Two spatial filters naturally arise. The first is the grid‑cell averaging filter. The second emerges from the interpolation of fluxes at cell faces, an inherent step in finite‑volume discretization. While the cell‑averaging filter suppresses subgrid‑scale motions, the interpolation filter plays a more subtle role: it determines which structures are treated as the resolved large eddies. Thus, the interpolation filter sets the operational resolution at which the flow is actually resolved. The net effect of smaller scales of motion is modelled. This model bridges physical and numerical interpretations which converge when filtering, modeling, and discretization are treated in a fully coherent manner - that is, as elements of a unified methodology. The two spatial filters yield a three‑way partition of kinetic energy into a subgrid component associated with motions smaller than the grid scale, a large‑eddy component corresponding to the resolved dynamics, and a supergrid component comprising scales removed by the cell‑to‑face interpolation. The latter scales do not constitute independent turbulent motions; rather, they are subordinate to the resolved large eddies. The model is formulated to ensure that the resolved large eddies do not generate unphysical smaller‑scale motions that lie beyond the representational capacity of the cell‑to‑face interpolation. Model consistency is further enhanced through extrapolation. The resulting framework is successfully tested on two canonical problems: one‑dimensional decaying Burgers turbulence, which provides a controlled setting for examining nonlinear energy transfer, and a three‑dimensional Taylor–Green vortex problem (Re=1600).