A novel iterative penalty method to enforce boundary conditions in Finite Volume POD-Galerkin reduced order models for fluid dynamics problems

TL;DR

This paper introduces an improved iterative penalty method for enforcing boundary conditions in finite volume POD-Galerkin reduced order models, demonstrating enhanced accuracy and significant computational speedups in fluid dynamics simulations.

Contribution

It presents a novel iterative solver for penalty factors in boundary condition enforcement within reduced order models, improving upon traditional tuning methods.

Findings

The penalty method achieves accuracy comparable to full models.

Reduced order models are 270-308 times faster for cavity flow.

The approach is effective for complex flow geometries like Y-junctions.

Abstract

A Finite-Volume based POD-Galerkin reduced order model is developed for fluid 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 and the penalty method where the boundary conditions are enforced in the reduced order model using a penalty factor. The penalty method is improved by using an iterative solver for the determination of the penalty factor rather than tuning the factor with a sensitivity 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 inlet channels and one outlet channel. The results show that the boundaries of the reduced order model can be controlled with the boundary control methods and the same order of accuracy is achieved for the velocity and pressure fields. Finally, the reduced order models are 270-308 times faster than the full order models for the lid driven cavity test case and 13-24 times for the Y-junction test case.