Métodos de elementos finitos híbridos para modelos RANS de turbulência

Abstract

This work explores hybrid finite element formulations for turbulent flows modeled by a system of partial differential equations governed by the combination of ReynoldsAveraged Navier-Stokes (RANS) equations with turbulence models. This system entails numerical challenges due to convective effects, nonlinearity, and high computational cost. To overcome these difficulties, we’ve devised a strategy employing hybrid finite element methods for RANS and turbulence models, using upwind and discontinuity-capturing schemes to counter convective effects and Newton and Picard methods for linearization. Thus, the resulting hybrid formulation is time-integrated using a first-order implicit method, while continuous for the Lagrange multiplier reduces computational expenses during global system assembly. In this context, classical turbulence flow problems such as plane jet, backward-facing step, and flow around an airfoil are simulated using the Standard k-ε models, as well as those proposed by Launder-Sharma and Chien and the one-equation Spalart-Allmaras model. The proposed solver methodology is extensively tested and validated against experimental data and/or numerical solutions from the open-source OpenFOAM software. The results for the k-ε model show a good agreement between the hybrid method, OpenFOAM approximations, and literature data. In the case of the Spalart-Allmaras model, except for the airfoil where relatively close results are observed, the approximations obtained by the hybrid formulation are in excellent agreement with the ones from OpenFOAM.