An efficient hyper reduced-order model for segregated solvers for geometrical parametrization problems

TL;DR

This paper introduces a hyper-reduced order modeling approach for segregated finite-volume solvers that significantly reduces computational costs in geometrically parametrized problems while maintaining high accuracy.

Contribution

The paper presents a novel hyper-reduction technique combined with segregated solvers and geometric parametrization, enabling fast and scalable CFD simulations.

Findings

Achieves near full-order accuracy with reduced computational time

Maintains efficiency across linear, nonlinear, and incompressible flow problems

Method is parallelizable and scalable to large meshes

Abstract

We propose an efficient hyper-reduced order model (HROM) designed for segregated finite-volume solvers in geometrically parametrized problems. The method follows a discretize-then-project strategy: the full-order operators are first assembled using finite volume or finite element discretizations and then projected onto low-dimensional spaces using a small set of spatial sampling points, selected through hyper-reduction techniques such as DEIM. This approach removes the dependence of the online computational cost on the full mesh size. The method is assessed on three benchmark problems: a linear transport equation, a nonlinear Burgers equation, and the incompressible Navier--Stokes equations. The results show that the hyper-reduced models closely match full-order solutions while achieving substantial reductions in computational time. Since only a sparse subset of mesh cells is evaluated during the online phase, the method is naturally parallelizable and scalable to very large meshes. These findings demonstrate that hyper-reduction can be effectively combined with segregated solvers and geometric parametrization to enable fast and accurate CFD simulations.