A P-DNS approach for weakly compressible turbulent flows

Turbulence modeling remains one of the most challenging problems in computational fluid dynamics due to the wide range of scales involved. The Pseudo-Direct Numerical Simulation (P-DNS) methodology offers a multiscale approach capable of resolving all turbulence scales while reducing the computational cost associated with fully resolved simulations. In this work, the P-DNS methodology is extended to weakly compressible flows, under the key assumption that the fine-scale dynamics can still be considered effectively incompressible. This assumption allows reusing the available fine-scale incompressible databases, which ensure a physically consistent and robust multiscale representation through two distinct representative volume elements for the flow behaviour near and far from walls, while leaving compressibility effects to be considered only at the coarse-scale level. Additionally, the memory model is reformulated into a single transport equation, facilitating its integration into compressible solvers and enabling a continuous representation of the inertial stress tensor time evolution. The extended P-DNS framework is validated against canonical test cases including flat plate boundary layers, axisymmetric subsonic jets (hot and cold), and the Common Research Model (CRM) aircraft configuration. Results demonstrate that P-DNS accurately predicts skin-friction, drag, velocity profiles, turbulent kinetic energy and shear stresses across these diverse flow configurations.