POD-Galerkin reduced order methods for combined Navier-Stokes transport equations based on a hybrid FV-FE solver
For researchers in computational fluid dynamics, this provides a reduced order modeling approach for coupled flow-transport problems on staggered meshes, though it is an incremental extension of existing POD-Galerkin methods.
This work introduces a POD-Galerkin reduced order model for coupled Navier-Stokes transport equations using a hybrid FV-FE solver with staggered meshes. The method is verified on 3D manufactured test cases and a modified cavity benchmark, achieving accurate pressure reconstruction via a Poisson equation.
The purpose of this work is to introduce a novel POD-Galerkin strategy for the hybrid finite volume/finite element solver introduced in Bermúdez et al. 2014 and Busto et al. 2018. The interest is into the incompressible Navier-Stokes equations coupled with an additional transport equation. The full order model employed in this article makes use of staggered meshes. This feature will be conveyed to the reduced order model leading to the definition of reduced basis spaces in both meshes. The reduced order model presented herein accounts for velocity, pressure, and a transport-related variable. The pressure term at both the full order and the reduced order level is reconstructed making use of a projection method. More precisely, a Poisson equation for pressure is considered within the reduced order model. Results are verified against three-dimensional manufactured test cases. Moreover a modified version of the classical cavity test benchmark including the transport of a species is analysed.