Impact of Structure-Preserving Discretizations on Compressible Wall-Bounded Turbulence of Thermally Perfect Gases

Abstract

Direct numerical simulations of compressible turbulent channel flow at supersonic and hypersonic Mach numbers are performed using a thermally perfect gas model for CO$_2$. The objective is to assess the role of structure-preserving discretizations of the convective terms in high-enthalpy regimes, with particular emphasis on entropy conservation, kinetic-energy preservation, and consistency with the thermodynamic closure. The comparative analysis of various formulations examines their impact on robustness, thermodynamic fluctuations, and turbulence statistics across a range of Mach numbers. Differences among formulations are found to originate primarily in the treatment of thermodynamic variables and progressively influence the dynamical fields as compressibility effects intensify. In particular, the coupling between entropy consistency and pressure discretization is shown to affect Reynolds stresses and mean flow properties in high-speed regimes. Overall, the results indicate that consistency between the numerical formulation and the thermodynamic model contributes significantly to the reliable simulation of high-enthalpy compressible turbulence. The study systematically assesses entropy-conservative discretizations for thermally perfect gases in wall-bounded flows and examines their impact on thermodynamic-dynamic coupling at high Mach numbers.