Requirement for Higher-Order Viscous Discretization to Avoid Numerical Contamination of Subgrid-Scale Model-Constant Estimates in a Linearly Forced Taylor-Flow Benchmark

This study quantifies how viscous-term discretization errors contaminate subgrid-scale (SGS) model-constant estimates when SGS eddy viscosity is tuned to satisfy an energy budget. A linearly forced, steady two-dimensional low-Reynolds-number Taylor-flow benchmark is used: it preserves global kinetic energy analytically, and the forcing cancels the viscous term without altering the convective–pressure balance when incompressibility holds. Large-eddy simulations on staggered grids (562–4802) employ second-, fourth- and sixth-order central differences for the viscous term and second- or fourth-order convective schemes. SGS stresses are represented by the Vreman model, used to probe numerical error–SGS interaction rather than to validate three-dimensional turbulence physics. Energy errors arise almost exclusively from the viscous discretization and scale as Δxm (m=2,4,6). Balancing this truncation error with SGS dissipation (∝CvΔx2) yields the theoretical scaling Cv∝Δxm−2. For a second-order viscous scheme, the required Cv becomes Δx-independent, Re-dependent, and far above practical LES values, showing that tuning can serve as a numerical band-aid and undermine quantitative constant estimation. With fourth- or higher-order viscous discretization, the required Cv decays rapidly with refinement; when Cv is adjusted, global energy is recovered and RMS velocity errors decay with viscous accuracy, while convective-order effects remain minor.