Análise e implementação de esquemas upwind polinomiais e suas aplicações em escoamentos de fluidos incompressíveis

Abstract

Several scientific and engineering problems about fluids are characterized by convective flows. Problems of this nature are challenging and require the development of efficient, robust and accurate numerical schemes. Thus, the topic has been one of the main concerns of the scientific community in the area of CFD (Computational Fluid Dynamics). Numerical solutions for this type of problem involve, among others, the development of numerical schemes for the treatment of the convective term and turbulence modeling. The present work aims to contribute to the numerical study and implementation of polynomial upwind schemes for the treatment of the convective term of partial differential equations and their applications in the flow of incompressible fluids. Therefore, this work aims to compare the polynomial upwind schemes TOPUS (“Third-Order Polynomial Upwind Scheme”), FSFL (“Flexible and Symmetric Flux Limiter”), SDPUS-C1 (“Six-Degree Polynomial Upwind Scheme”) and EPUS (“Eight-degree Polynomial Upwind Scheme”) together using computational experiments with parameter variation. One-dimensional problems are numerically solved through computational implementation using the finite difference method and formulation in normalized variables. Two-dimensional fluid flow simulations are performed using OpenFOAM, through the finite volume method and formulation in flow limiters for the schemes. This work aims to study and implement advanced polynomial upwind schemes as well as their incorporation into the OpenFoam tool. An important contribution of this work is the implementation and study of the FSFL scheme through computational experiments, providing new results and comparisons not seen in the literature so far. The results obtained with the performed experiments show that both the TOPUS, FSFL, SDPUS-C1 and EPUS schemes provide good results for the treatment of the convective term of transport equations. The EPUS scheme performed better in terms of accuracy and the TOPUS scheme stood out by achieving a minimum temporal residual with fewer iterations. In addition, the SDPUS-C1 scheme proved to be very effective both in terms of accuracy and iterations to reach an established minimum time residual.