A multiscale Pseudo-DNS approach for solving turbulent boundary-layer problems

Abstract

Efficiently simulating turbulent fluid flow within a boundary layer is one of the major challengesin fluid mechanics. While skin friction may have a limited impact on drag at high Reynoldsnumbers, it plays a crucial role in determining the location of fluid separation points. Shiftsin these separation points can dramatically alter drag and lift, underscoring the importanceof accurately accounting for viscous effects. It is generally accepted that the Navier–Stokesequations contain all the necessary physical ingredients to accurately simulate fluid flows, evenin complex scenarios. With a sufficiently fine mesh, we could simulate all fluid flows withoutrelying on additional empirical approximations. However, this Direct Numerical Simulation(DNS) strategy is computationally impractical with current technology. The Pseudo-DNS (P-DNS) method offers a novel approach to solve the governing equations with the mesh refinementneeded to achieve DNS-level accuracy. The solution is divided into fine and coarse scales,and through an iterative process, both scales are solved until convergence. Computationalcost is affordable due to parametrize and solving the fine scale under different boundaryconditions in simple domains, which allows performing these calculations offline – prior toand independent of the global solution – only once. The key novelty introduced in this work isthe wall representative volume element (RVE), which models the time developing of turbulentboundary layers and its outputs can be adapted for adverse and favorable pressure gradientscenarios. The multiscale method enables accurate prediction of aerodynamic forces usingrelatively coarse meshes for boundary layers, without the need for empirical parameters orcase-specific models. Several case studies involving 2D and 3D flows over both streamlined andbluff bodies validate the ability of P-DNS to deliver reliable results while maintaining modestcomputational requirements.