Directional Residual Stabilization for High–Peclet-Number Advection–Diffusion Problems: GPU-Accelerated Implementation in the Vanadis System

This preprint develops a directional residual stabilization method tailored for high–Peclet-number advection–diffusion problems, addressing numerical instabilities typical of convection‑dominated regimes. The formulation is integrated into the GPU‑accelerated Vanadis finite‑element system, enabling efficient large‑scale simulations. The work provides implementation strategies, and benchmark results demonstrating improved stability, accuracy, and computational performance. The method is applied within a fully three‑dimensional atmospheric dispersion model, where the GPU implementation enables real‑time evaluation of pollutant transport scenarios.