An Optimized Algorithm for the Mitigation of Numerical Oscillations in Engineering Simulations: A Case Study in Grain Aeration Modeling

ABSTRACT Spurious oscillations are a recurring challenge in numerical simulations of advection‐dominated transport, often degrading stability and predictive accuracy. Artificial viscosity is commonly employed to mitigate these effects, but its coefficient is usually tuned empirically, limiting reproducibility and scalability. This study introduces a predictive framework in which the viscosity coefficient is derived analytically from discretization parameters through a closed‐form law obtained via offline optimization guided by a smoothness metric. The methodology is demonstrated for grain aeration, a coupled heat‐moisture transport problem of high practical relevance. The mathematical model was solved using finite differences with the Leith scheme, known for enhanced robustness under realistic aeration conditions. Verification based on apparent order‐of‐convergence analysis of the discretization error confirmed that the stabilized formulation recovered second‐order accuracy, while the unstabilized model exhibited order degradation. Validation against experimental data showed accuracy comparable to manual calibration but with greater stability. Smoothness analysis revealed oscillations only in the energy balance, with mass‐balance equations remaining naturally smooth. Once trained, the predictive law added negligible computational cost (3.5 s per run vs. 162.1 s for mesh refinement ‐ a well‐known technique for reducing oscillations in numerical solutions). The approach eliminates empirical tuning, ensures convergence under experimental conditions, and achieves substantial computational savings for coupled transport problems.