Incompressible Viscous Flow Analysis and Adaptive Finite Element Method Using Linear Bubble Function

Abstract

A new finite element formulation and adaptive remeshing method with linear bubble function for the incompressible Navier-Stokes equations are proposed in this paper. As the numerical approach, the spacial discretization is applied the mixed interpolations for velocity and pressure fields by the bubble element and linear element, respectively. The fractional step method based on the implicit time integration is used for the discretization. To verify applicabilityof presented linear bubble function, Rayleigh-Benard convection and flow past a circular cylinder are performed for the numerical examples.