Separated response surfaces for flows in parametrised domains: comparison of a priori and a posteriori PGD algorithms

TL;DR

This paper compares a priori and a posteriori PGD algorithms for reduced order modeling of incompressible Stokes flows in geometrically parametrized domains, highlighting their accuracy and computational efficiency across varied parameters.

Contribution

It provides a comprehensive comparison of a priori and a posteriori PGD algorithms for complex parametrized flow problems, which was previously lacking.

Findings

A posteriori PGD achieves higher accuracy in complex geometries.

A priori PGD requires fewer full-order solves for similar accuracy.

Performance varies significantly with geometric parameter ranges.

Abstract

Reduced order models (ROM) are commonly employed to solve parametric problems and to devise inexpensive response surfaces to evaluate quantities of interest in real-time. There are many families of ROMs in the literature and choosing among them is not always a trivial task. This work presents a comparison of the performance of a priori and a posteriori proper generalised decomposition (PGD) algorithms for an incompressible Stokes flow problem in a geometrically parametrised domain. This problem is particularly challenging as the geometric parameters affect both the solution manifold and the computational spatial domain. The difficulty is further increased because multiple geometric parameters are considered and extended ranges of values are analysed for the parameters and this leads to significant variations in the flow features. Using a set of numerical experiments involving geometrically parametrised microswimmers, the two PGD algorithms are extensively compared in terms of their accuracy and their computational cost, expressed as a function of the number of full-order solves required.