Hybridisable discontinuous Galerkin solution of geometrically parametrised Stokes flows

TL;DR

This paper introduces a high-order hybridisable discontinuous Galerkin method combined with proper generalised decomposition to efficiently solve and analyze geometrically parametrised Stokes flow problems in multiple dimensions.

Contribution

It presents a novel computational framework that constructs a comprehensive off-line solution for parametrised flows, improving upon existing methods for sensitivity analysis and geometric variations.

Findings

Demonstrates optimal approximation properties of the method.

Shows applicability in 2D and 3D flow problems.

Provides efficient off-line solutions for multiple geometric parameters.

Abstract

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 approximation properties of the proposed method and demonstrate its applicability in two and three dimensions.