Response of the structure under the effect of fluid flow by the edge-based smoothed finite element method (es-fem)

Nguyễn Hoàng Sơn, Liêu Quân Quí, Phùng Văn Phúc, Nguyễn Thời Trung
Hội nghị Cơ học toàn quốc lần thứ IX Hà Nội, 8-9/12/2012

Abstract
The paper presents a combined numerical method for analyzing the response of the structure under the effect of two-dimensional fluid flow. The structure is solved approximatedly by the edge-based smoothed finite element method using linear triangular elements (ES-FEM-T3). The fluid flow is represented by the incompressible Newtonian fluid flow governed by the Navier-Stokes equations and is solved approximatedly by the mixed finite element method P2P1 using triangular elements (six velocity nodes and three pressure nodes). The time approximation in the unsteady Navier-Stokes equations is discretized by the implicit difference method using a stabilized trapezoid rule. The Picard iteration is used to solve the steady Navier-Stokes equations and the adaptive time-stepping algorithm is used to solve the unsteady Navier-Stokes equations in which the nonlinear convection term is approximated into an explicit linearization. The structural and fluid domains are discretized independently, so the nodes at the structurefluid interface can be divided separately.The fluid forces at the structure-fluid interface are approximated into a polynomial function,and then transformed into nodal forces applied to the structure.The numerical examples in the paper are analyzed by the Matlab programming, and then compared and verified with the results of COMSOL and ANSYS softwares.

Keywods: Edge-based smoothed finite element method (ES-FEM), Navier-Stokes equations, Newtonian fluid, incompressible flow, Fluid-StructureInteraction (FSI).