Nonintrusive proper generalised decomposition for parametrised incompressible flow problems in OpenFOAM

Abstract

The computational cost of parametric studies currently represents the major limitation to the application of simulation-based engineering techniques in a daily industrial environment. This work presents the first nonintrusive implementation of the proper generalised decomposition (PGD) in OpenFOAM, for the approximation of parametrised laminar incompressible Navier-Stokes equations. The key feature of this approach is the seamless integration of a reduced order model (ROM) in the framework of an industrially validated computational fluid dynamics software. This is of special importance in an industrial environment because in the online phase of the PGD ROM the description of the flow for a specific set of parameters is obtained simply via interpolation of the generalised solution, without the need of any extra solution step. On the one hand, the spatial problems arising from the PGD separation of the unknowns are treated using the classical solution strategies of OpenFOAM, namely the semi-implicit method for pressure linked equations (SIMPLE) algorithm. On the other hand, the parametric iteration is solved via a collocation approach. The resulting ROM is applied to several benchmark tests of laminar incompressible Navier-Stokes flows, in two and three dimensions, with different parameters affecting the flow features. Eventually, the capability of the proposed strategy to treat industrial problems is verified by applying the methodology to a parametrised flow control in a realistic geometry of interest for the automotive industry.

Nonintrusive reduced order model for parametric solutions of inertia relief problems

“…Clearly, this quantity is strictly related to the production cost. The objective function g 2 ( ) represents the parametric ETS defined in Equation (41).…”

“…One of the main drawbacks of the original PGD approach, when compared to other a posteriori approaches, is the intrusivity of its implementation, which precludes its wider application in an industrial context, where commercial software are usually employed. This limitation has motivated the development of nonintrusive implementations of the PGD rationale for solid 40 and fluid 41 mechanics problems. Also motivated by the goal of achieving the nonintrusive applications of the PGD, the Encapsulated PGD Toolbox has been recently developed by Díez et al 42,43 The toolbox consists of a collection of PGD-based routines that are able to perform algebraic operations for multidimensional tensors.…”

“…Geometry of the body in white with three car components highlighted. The parameters correspond to the thickness of each one of the components F I G U R E 14 Illustration of the angles used to compute the equivalent torsional stiffness in Equation(41) …”

Hybrid Neural Network Reduced Order Modelling for Turbulent Flows with Geometric Parameters

“…ROMs can be classified depending on the technique used to approximate the solution manifold and the method used to evolve the latent dynamics. The most used techniques to evaluate the solution manifold are based on linear approximation methods such as the reduced basis with a greedy approach [3,4], the proper orthogonal decomposition [5], or nonintrusive methods as exposed in [6], but more recently nonlinear methods have also been proposed [7,8]. Concerning the evolution of the latent space dynamics, arguably the most common approach is based on the (Petrov-) Galerkin projection of the original system onto the reduced subspace/manifold [9].…”

Spurious-free interpolations for non-intrusive PGD-based parametric solutions: Application to composites forming processes

“…The assigned problems are managed by classical PGD decomposition procedures [1,6,11]. Another way of constructing a computational vademecum through the use of non-intrusive PGD relies on the calculation of snapshots to later on construct a manifold of solutions using the locally linear embedding (LLE) for example or other manifold learning techniques [2,4,5,12,15,17,21,23]. Despite numerous developments during the recent years towards the development of computational vademecums in both intrusive and non-intrusive manners [11], the calculation of solution handbooks using any of the aforementioned methods faces a major challenge when changing a parameter induces drastic changes in the solution map.…”