Numerical simulation of a rising bubble in viscoelastic fluids

In this paper we discuss simulation techniques for a rising bubble in viscoelastic fluids via numerical methods based on high order FEM. A level set approach based on the work in [9] is used for interface tracking between the bubble and the surrounding fluid. The two matters obey the Newtonian and the Oldroyd-B constitutive law in the case of a viscoelastic fluid while the flow model is given by the Navier-Stokes equations. The total system of equations is discretized in space by the LBB-stable finite element Q2P1, and in time by the family of θ−scheme integrators. The solver is based on Newton-multigrid techniques [1,2] for nonlinear fluids. First, we validate the multiphase flow results with respect to the benchmark results in [4], then we perform numerical simulations of a bubble rising in a viscoelastic fluid and show cusp formation at the trailing edge.