A Novel Iterative Penalty Method to Enforce Boundary Conditions in Finite Volume POD-Galerkin Reduced Order Models for Fluid Dynamics Problems (Communications in Computational Physics, 2021)
A Finite-Volume based POD-Galerkin reduced order model is developed forfluid dynamics problems where the (time-dependent) boundary conditions are controlled using two different boundary control strategies: the lifting function method,whose aim is to obtain homogeneous basis functions for the reduced basis space andthe penalty method where the boundary conditions are enforced in the reduced ordermodel using a penalty factor. The penalty method is improved by using an iterativesolver for the determination of the penalty factor rather than tuning the factor with asensitivity analysis or numerical experimentation.The boundary control methods are compared and tested for two cases: the classical lid driven cavity benchmark problem and a Y-junction flow case with two inletchannels and one outlet channel. The results show that the boundaries of the reducedorder model can be controlled with the boundary control methods and the same orderof accuracy is achieved for the velocity and pressure fields. Finally, the reduced ordermodels are 270-308 times faster than the full order models for the lid driven cavity testcase and 13-24 times for the Y-junction test case.
Keywords: Proper Orthogonal Decomposition; Navier–Stokes equations; Galerkin projection; penalty method; lifting function method; iterative method.