Finite elements with node dependent kinematics and scalable accuracy for the analysis of Stokes flows

Abstract

This paper extends the use of one-dimensional elements with node-dependent kinematics to the analysis of Stokes flows. According to the Carrera Unified Formulation, the primary variables of the flow, velocity and pressure, are expressed as arbitrary expansions of the generalized unknowns. The novel implementation proposed in this work allows to increase the accuracy of the model only in the areas of the domain where it is required; i.e. close to boundaries, barriers or sudden expansion. Refined one-dimensional models based on Taylor and Lagrange expansions are used in this work and some typical applications are proposed to assess this novel technique, including Stokes flows in cylindrical and non-conventional domains. For each numerical example, different combinations of one-dimensional models have been considered to account for different kinematic approximations of flows, and the results, compared with analytical or finite volume solutions, highlight the capabilities of the proposed approach to handle non-conventional boundary conditions with ease and in preserving the computational cost without any accuracy loss.