Proper orthogonal decomposition closure models for Burgers and Navier-Stokes equations

摘要

Proper orthogonal decomposition based reduced-order models hold importance in fluid dynamics due to their utilization in flow control, design, and optimization. The reduced-ordered models have shown promising results for laminar flows, however, lack accuracy for complex and turbulent flows. In this study, we consider Burgers and Navier-Stokes equations and develop their reduced order models. Burgers equation is considered with homogenous boundary condition and Navier-Stokes equations are used for simulating the incompressible fluid flow past a circular cylinder. The literature shows that the conventional reduced-order models do not perform well in case of less number of modes and require closure model for the discarded modes. We investigate the effect of closure modeling on the accuracy of the reduced-order model for 1D Burgers equation and 2D Navier-Stokes equations. We consider three mode-dependent closure models, based on eddy viscosity model. This study compares the performance of all considered closure models for wide range of mathematical parameter v_e and choose the best closure approach for the reduced-order model of Navier-Stokes equations. The numerical results show that the selected closure model greatly improves the accuracy of the reduced-order model for both Burgers and Navier-Stokes equations.