Modelagem matemática e computacional de escoamentos turbulentos usando a metodologia mista pseudoespectral de fourier e fronteira imersa

Abstract

Turbulence in fluid flows is one of the most complex and relevant physical phenomena in engineering, and its computational modeling demands high-fidelity and computationally efficient methodologies. In this context, the present thesis proposes the development, verification, and validation of two novel three-dimensional computational codes based on the IMERSPEC methodology, a hybridization of the Fourier Pseudospectral Method (MPF) and the Immersed Boundary Method (MFI), for the simulation of laminar and turbulent complex flows in the presence of walls. The developed codes, referred to as IMERSPEC MPI and IMERSPEC CUDA, are distinguished by their parallelization strategies: the former employs the MPI library with parallelization along two of the three flow directions, while the latter exploits heterogeneous CPU/GPU parallelism through the CUDA API, performing all computations entirely on the graphics processing unit. Both codes were computationally verified using the Method of Manufactured Solutions (MSM) for the isolated MPF and for the MPF coupled with the MFI in coincident and non-coincident grid configurations, achieving spectral accuracy and fourth-order convergence, respectively. Additionally, the Spectral Direct Imposition Method (MIED) was proposed and investigated as a fully spectral alternative to the MDFM for non-coincident grids, whose results indicated lower accuracy than the MDFM at comparable computational cost. The physical validation of both codes was carried out through the simulation of laminar flow over a backward-facing step, a classical complex flow benchmark, with results consistent with experimental reference data. Comparing the two codes under identical simulation conditions on different hardware configurations, the IMERSPEC CUDA outperformed the IMERSPEC MPI across all evaluated mesh sizes, achieving a computational cost reduction of approximately twenty-nine times for the laminar case. It is emphasized that this result is obtained when comparing the IMERSPEC MPI executed on a cluster with 64 processes and the IMERSPEC CUDA running on the NVIDIA A100 GPU. On the other hand, it is noted that optimal execution parameters for the IMERSPEC CUDA code must be determined according to the GPU to be used, i.e., the optimal execution parameters are hardware-dependent. Based on the selection of the higher-performance code, subsequent developments for Large Eddy Simulation (LES) modeling were conducted exclusively with the IMERSPEC CUDA. In the turbulent flow simulations, the interaction between the IMERSPEC methodology and the LES approach was investigated, identifying and correcting implementation aspects that prevented the correct reproduction of turbulent flow, such as the restructuring of the complementary domain, the adoption of an exponential filter for the dealiasing procedure, and the definition of the top boundary conditions of the computational domain. Three functional subgrid-scale (SGS) closure models were implemented and compared for turbulent flow over a backward-facing step at Reynolds number Re_H = 5100: the classical Smagorinsky model with Van Driest damping functions, the WALE model (Wall-Adapting Local Eddy-viscosity), and the Germano-Lilly dynamic model. Results obtained with meshes of $32\times128\times256$ and $64\times256\times512$ collocation points were compared against computational and experimental reference data. The WALE model demonstrated the best overall performance, with an error of only 0,5% in the reattachment length estimation and the lowest computational cost among the three evaluated models, making it the most suitable choice for the present simulations, although this subgrid-scale model presents mean velocity profiles and Boussinesq-Reynolds mean stress tensor components with significant discrepancies relative to reference data. The Germano-Lilly dynamic model yielded results slightly superior to those of the classical Smagorinsky model, with reattachment length errors of 11% and 13%, respectively, at a higher computational cost. The IMERSPEC CUDA with the LES approach and the Germano-Lilly dynamic model, the most computationally demanding configuration, reproduced 450 s of physical time in less than 72 hours on the NVIDIA A100 GPU, demonstrating the viability of the methodology for high-order simulations within competitive computational time.