Direct Numerical Simulation of High-Speed Turbulent Boundary Layers: Current State and Future Challenges

High-speed turbulent boundary layers govern the transport of momentum, mass, and energy in compressible flows and play a central role in determining aerodynamic performance, skin-friction drag, aerodynamic heating, flow stability, and thermal protection requirements of advanced aerospace vehicles. Over the past three decades, direct numerical simulation (DNS) has revolutionized the study of compressible wall-bounded turbulence by resolving all dynamically relevant turbulent scales without turbulence-model assumptions, providing benchmark-quality databases and unprecedented physical insight into flow phenomena that remain difficult or impossible to measure experimentally. Together with complementary high-fidelity approaches, DNS has substantially advanced the understanding of turbulence dynamics across a broad range of supersonic and hypersonic flow conditions. This review presents a critical assessment of advances in the high-fidelity simulation of compressible turbulent boundary layers under non-reacting conditions. Particular emphasis is placed on the flow physics of canonical zero-pressure-gradient boundary layers, shock-wave/turbulent-boundary-layer interactions (SWTBLIs), pressure-gradient-driven flows, streamline-curvature effects, and thermochemical non-equilibrium phenomena. Recent developments in numerical methodologies are also briefly examined, including high-order discretization techniques, turbulence inflow generation methods, hybrid continuum-kinetic formulations, and advances in high-performance computing that have enabled DNS at increasingly high Reynolds and Mach numbers. The review highlights the major physical insights emerging from DNS studies, demonstrating that many fundamental characteristics of compressible wall turbulence remain closely related to their incompressible counterparts when appropriate compressibility transformations are employed. At the same time, DNS has revealed the critical influence of wall temperature, pressure gradients, streamline curvature, shock interactions, and finite-rate thermochemistry on turbulence structure, coherent motions, interscale energy transfer, boundary-layer separation, and aerodynamic heating.