Wall modeling via function enrichment for finite-volume Reynolds-averaged Navier–Stokes simulations of compressible turbulent flows at moderate Mach numbers

Accurately simulating high-Reynolds number compressible wall-bounded turbulent flows is computationally intensive, primarily due to the fine grid resolution required to capture the steep velocity gradients in the near-wall region. To address this challenge, we propose a wall modeling technique that incorporates function enrichment within the finite volume framework for efficient Reynolds-averaged Navier–Stokes (RANS) simulations of compressible wall-bounded turbulent flows. The function enrichment approach integrates a wall function that approximates the sharp streamwise velocity profile in the wall-normal direction, thereby enhancing the solution space of the finite volume method. By incorporating this wall function, turbulent features in the near-wall region can be accurately captured even on coarse grids. Our analysis of compressible turbulent flat plate boundary layers demonstrates that function enrichment can effectively model the momentum and total energy variables in flows with moderate Mach numbers (less than three), using a simple wall function originally developed for incompressible flows. The piece-wise approximation of the solution in the enriched function space can be determined using a variational reconstruction. A preliminary analysis reveals that discontinuities are unlikely to occur in the boundary layer, facilitating straightforward shock capturing by eliminating the need for limiting in cells with function enrichment. Numerical results of benchmark test cases demonstrate that the variational finite volume RANS solver with function enrichment can accurately simulate compressible wall-bounded turbulent flows at moderate Mach numbers, even on computational meshes with coarse near-wall grids. The function enrichment improves skin-friction prediction accuracy by one to two orders of magnitude in most test cases.