A residual-based stabilized finite element formulation for incompressible flow problems in the Arlequin framework

Abstract

Many fluid flow problems involve localized effects within a larger flow domain, with boundary layers close to solid boundaries being one of the most common. Accurate and realistic computational analysis of such problems requires that the local flow behavior be properly represented by a numerical formulation with affordable computational cost. Among several strategies developed in the computational mechanics to deal with multiscale phenomena, the Arlequin method proposes overlapping a local discretization to a global one, in the neighborhood of localized effects, and gluing both models in an appropriate subzone of the overlap by means of Lagrange multipliers method, being successful in the solid mechanics context, but less explored in CFD analysis. To improve stability and conditioning of the algebraic system of equations and, at the same time ensure more flexibility, we propose a novel residual-based stabilized Arlequin formulation. Following, the proposed formulation is applied to the numerical analysis of incompressible flows. The resulting formulation is tested with selected numerical examples, considering structured and unstructured, coincident and non-coincident finite element discretization, Stokes problems and convection dominated Navier–Stokes problems, steady and transient cases, showing the methodology precision, robustness and flexibility.