Hybridisable discontinuous Galerkin solution of geometrically parametrised Stokes flows

Author (s): Sevilla, R., Borchini, L., Giacomini, M. and Huerta, A.
Journal: Computer Methods in Applied Mechanics and Engineering

Volume: 372
Date: 2020

This paper proposes a novel computational framework for the solution of geometrically parametrised flow problems governed by the Stokes equation. The proposed method uses a high-order hybridisable discontinuous Galerkin formulation and the proper generalised decomposition rationale to construct an off-line solution for a given set of geometric parameters. The generalised solution contains the information for all the geometric parameters in a user-defined range and it can be used to compute sensitivities. The proposed approach circumvents many of the weaknesses of other approaches based on the proper generalised decomposition for computing generalised solutions of geometrically parametrised problems. Four numerical examples show the optimal mesh convergence properties of the proposed method and demonstrate its applicability in two and three dimensions, with particular emphasis on parametrised flows in microfluidics.



        Author = {Ruben Sevilla and Luca Borchini and Matteo Giacomini
              and Antonio Huerta},
        Title = {Hybridisable discontinuous {G}alerkin solution of 
                 geometrically parametrised {S}tokes flows},
        Fjournal = {Computer Methods in Applied Mechanics and Engineering},
        Journal = {Comput. Methods Appl. Mech. Eng.},
        Volume = {372},
        Pages = {113397},
        Year = {2020},
        Doi = {10.1016/j.cma.2020.113397}