Natural convection of incompressible viscoelastic fluid flow

Abstract

We revisit the MIT Benchmark 2001 and introduce a viscoelastic constitutive law into the fluid in motion. Our goal is to study the effect of viscoelasticity into the periodical behavior of the physical quantities of the corresponding benchmark. We use a robust numerical technique in simulating complex fluid flow problems based on higher order Finite Element discretization. While marching in time, an A-stable method of second order is favorable, i.e Crank-Nicolson scheme, to reproduce periodical behaviors. We use a differential form of viscoelastic model, i.e Oldroyd-B type and find out that a small amount of viscoelasticity reduces the oscillatory behavior.