Closure in reduced-order model of Burgers equation

Proper orthogonal decomposition based reduced-order models is a significant model reduction technique in computational fluid dynamics, which are used in many industrial and practical applications e.g., flow control, design, and optimization. The reduced-ordered model works well for laminar flows however, lacks accuracy for complex and turbulent flows. In this paper, we use the 1D and 2D Burgers equations as surrogate for Navier-Stokes equations of fluid flow. We investigate the effect of closure modeling on the accuracy of reduced-order model for 1D and 2D Burgers equations. We consider homogenous and non-homogenous boundary conditions for 1D and 2D Burgers equations, respectively. Conventional reduced-order models do not perform well with less number of modes and require closure model for the discarded modes. Numerical results show that the closure model based on mixing length approach greatly improves the accuracy of the reduced-order model.