Finite Element Models of One Dimensional Flows With Node-Dependent Accuracy

Abstract

The formulation of simplified models in the description of flow fields can be highly interesting in many complex network such as the circulatory system. This work presents a refined one-dimensional finite element model with node-dependent kinematics applied to incompressible and laminar flows. In the framework of 1D-FE modelling, this methodology is a new development of the Carrera Unified Formulation (CUF), which is largely employed in structural mechanics. According to the CUF, the weak formulation of the Stokes problem is expressed in terms of fundamental nuclei and, in this novel implementation, the kinematics can be defined node by node, realizing different levels of refinements within the main direction of the pipe. Such feature allows to increase the accuracy of the model only in the areas of the domain where it is required, i.e. particular boundary condition, barriers or sudden expansion. Some typical CFD examples are proposed to validate this novel technique, including Stokes flows in uniform and non-uniform domains. For each numerical example, different combinations of 1D models have been considered to account for different kinematic approximations of flows, and in particular, models based on Taylor and Lagrange expansion have been used. The results, compared with ones obtained from uniform kinematics 1D models and with those come from available tools, highlight the capability of the proposed model in handling non-conventional boundary conditions with ease and in preserving the computational cost without any accuracy loss.