Data Assimilation of Compressibility Corrections in Spalart–Allmaras Turbulence Model for Hypersonic Flow

Accurate aerothermodynamic prediction in hypersonic shock–boundary-layer interaction (SBLI) flows remains challenging for Reynolds-averaged Navier–Stokes turbulence models, largely due to uncertainties in compressibility corrections. This study develops a data-assimilation framework using the ensemble Kalman filter to assess compressibility-related corrections in the Spalart–Allmaras (SA) turbulence model. By assimilating experimental wall heat-flux measurements, the coefficients of six compressibility-correction terms are treated as uncertain parameters and inferred using a hypersonic compression-corner configuration. The posterior estimates favor near-full activation of the density-gradient-related mixed-transport correction, moderate contributions from compressible dissipation and density-gradient diffusion, and suppression of the higher-order gradient-coupling correction. Analysis of the complete optimized terms shows that the mixed-transport term has the largest integrated magnitude over the selected SBLI region, although it is not locally dominant throughout the flowfield. Without further tuning, it maintains good agreement with experimental pressure and heat-flux distributions for a 15 deg compression corner and reduces velocity- and temperature-profile discrepancies relative to SA–Catris in two hypersonic flat-plate cases. These results suggest that the calibrated correction balance remains useful for the examined hypersonic configurations, although broader assessments with additional observables and flow conditions are required before claiming general applicability.