Grid resolution requirements for DNS of shock/boundary-layer interactions

Direct Numerical Simulation (DNS) of shock-boundary-layer interactions (SBLI) is critical for accurate prediction of turbulence, heat transfer, and separation in high-speed flows. One of the main challenges is selecting a grid resolution that properly resolves both pre- and post-interaction states while maintaining computational efficiency. This study systematically examines the impact of grid resolution on DNS accuracy, with particular focus on the post-interaction region, where turbulence length scales undergo a dramatic reduction-especially under hypersonic flow conditions. Through a series of high-fidelity simulations using grids of increasing resolution, we quantify the consequences of under-resolution on turbulence statistics, skin friction, and heat transfer, and demonstrate that classical DNS criteria remain applicable in SBLI once the viscous length scale reduction across the shock is properly accounted for. To support mesh design, we propose and validate a simple predictive scaling law, based solely on inviscid flow quantities, that estimates this reduction and thus enables a priori resolution requirements to be determined across different configurations. These results go beyond confirming the need for fine grids, providing a predictive tool to guide future DNS and wall-modeled LES of hypersonic SBLI.