Abstract: The One-Dimensional Turbulence (ODT) method is a turbulence modeling method that follows the basic physical laws of turbulence in the one-dimensional computational domain. The statistical laws of turbulence can be accurately captured in the one-dimensional computational domain by combining deterministic and stochastic solving methods, and modeling in the reduced dimension can significantly reduce the amount of computation. The ODT method is widely used in the study of incompressible turbulence and turbulent combustion, but needs to be further improved to simulate high-speed compressible turbulent flows. Different from the incompressible ODT method, in this paper, the dependent variables are changed from the original variables to the conservative fluxes based on the Euler reference frame, which is beneficial to reducing the error of compressible turbulence simulation. A component solution module is also proposed in this research. A conservative compressible ODT method capable of simulating scalar mixing is developed by further improving both deterministic and stochastic solving modules in a corresponding manner. In the deterministic module, the one-dimensional truncated governing equations solved are adjusted as the ones with conservative fluxes as dependent variables, and the triplet mapped object is correspondingly changed from the original variables to the conservative fluxes, and simultaneously the kernel transformation with two kernels is selected to ensure momentum conservation for variable density when one-dimensional eddies are constructed in the stochastic module. The accuracy of the method for capturing scalar mixing in the compressible shear turbulent field was verified by simulating the spatially developing supersonic plane turbulent mixing layer and comparing the results of the self-similar stage with the experimental results. The mean profile and the fluctuation intensity profile of velocity field and component field captured by the method proposed are in excellent agreement with experimental results. The accuracy of the proposed method is obviously better than that of the Large Eddy Simulation with the Gradient Diffusion sub-grid closure (LES-GRAD.DIFF.) and that of the Large Eddy Simulation coupled with the Linear Eddy Mixing (LEM) model (LES-LEM), and the dimensionality reduction of the method proposed gives it a significant advantage in reducing computational cost.

Key words: One-Dimensional Turbulence (ODT), compressible turbulent flow, numerical simulation, conservative, mixing layer, scalar mixing