On the edge‐based smoothed finite element approximation of viscoelastic fluid flows

Abstract

This article discusses the numerical simulation of viscoelastic fluid flows using the edge-based smoothed finite element method (ESFEM). The incompressible Navier-Stokes equations coupled with the Oldroyd-B constitutive relation are decoupled via the characteristic-based split scheme that enables the use of equal-order interpolation for the triple primitive variables. For this reason, the spatial discretization is implemented with linear three-node triangular elements which work very well with the ESFEM. Edge-based smoothing cells (SCs) are constructed on grounds of existing elements, directly underpinning the essential gradient smoothing procedure. New integration points are proposed within local SCs since the ESFEM enjoys the tremendous flexibility of the smoothed Galerkin weak-form integral. The discrete viscoelastic system is entirely formulated in the edge-based notion such that all gradient-related terms are readily smoothed cell-by-cell. Finally, several numerical examples are presented to demonstrate the desirable capability of the ESFEM.

An edge‐based smoothed finite element framework for partitioned simulation of vortex‐induced vibration problems

“…The ESFEM has immediately succeeded in the numerical modeling of incompressible fluid flow and FSI 44 . It has been extended to viscoelastic fluid flow calculations almost at the same time 45 . The present study aims to further the ESFEM by simulating flow‐induced oscillations of multiple bluff bodies.…”

“…44 It has been extended to viscoelastic fluid flow calculations almost at the same time. 45 The present study aims to further the ESFEM by simulating flow-induced oscillations of multiple bluff bodies. Rigid and elastic structures are taken into account to interact with an incompressible viscous Newtonian fluid, respectively.…”

Application of Efficient Algorithm in Dynamic Simulation of Viscoelastic Fluid in 3D Animation

“…Among them, fluid simulation is an important research field in computer graphics, which is very important for simulating and rendering real-world fluid phenomena [1]. In the entertainment fields such as movies and games, in order to improve the audience's visual experience, animation needs more and more detailed and realistic fluid simulation effects [2]. At the same time, in the fields of scientific calculation and engineering simulation, it is also necessary to accurately simulate the fluid to guide the process of product design and optimization.…”