POD-Galerkin reduced order methods for combined Navier-Stokes transport\n equations based on a hybrid FV-FE solver

Abstract

The purpose of this work is to introduce a novel POD-Galerkin strategy for\nthe hybrid finite volume/finite element solver introduced in Berm\\'udez et al.\n2014 and Busto et al. 2018. The interest is into the incompressible\nNavier-Stokes equations coupled with an additional transport equation. The full\norder model employed in this article makes use of staggered meshes. This\nfeature will be conveyed to the reduced order model leading to the definition\nof reduced basis spaces in both meshes. The reduced order model presented\nherein accounts for velocity, pressure, and a transport-related variable. The\npressure term at both the full order and the reduced order level is\nreconstructed making use of a projection method. More precisely, a Poisson\nequation for pressure is considered within the reduced order model. Results are\nverified against three-dimensional manufactured test cases. Moreover a modified\nversion of the classical cavity test benchmark including the transport of a\nspecies is analysed.\n