Comparing Implicit Time-Stepping Techniques for Highly Resolved Simulations using Industrial Geometries

• First application and demonstration of two implicit time-stepping schemes on industrial geometries using high-order spectral/hp element discretization • Both schemes reduce computational cost up to 14.7 × less than a reference using community standard semi-implicit scheme • Timestep sensitivity analysis, verification with reference, and validation with experiments • Guidelines for leveraging these schemes for scale-resolving industrial simulations High-fidelity modeling approaches such as implicit Large Eddy Simulations are increasingly used for analyzing complex, unsteady flow phenomena in industrial geometries at realistic Reynolds numbers. However, their computational cost prevents wider adoption as a suitable tool in developing aerodynamic devices. One solution available to most commercial tools is to increase the simulation timestep, beyond the CFL limit of commonly adopted semi-implicit scheme, by employing fully implicit time discretization. Two implicit time-stepping techniques for solving the incompressible Navier-Stokes equations in a segregated manner using the high-order Spectral/hp element method were examined in this study. Our objectives were to explore the practical timestep limit for each scheme, assess the impact of timestep on accuracy, and evaluate the potential speed-up. The Imperial Front Wing (IFW) industrial benchmark was considered for these purposes. Even for this challenging geometry, both schemes successfully allowed for an increased simulation timestep, resulting in a considerable reduction in the total computation time. This work outlines the characteristics of each scheme, compares them with existing literature on canonical flows, and highlights the trade-offs between accuracy and computational efficiency.