A material point method for simulation of viscoelastic flows

A novel variant of the Material Point Method is proposed to solve flow problems for incompressible viscoelastic fluids. As in the original spirit of the method, material points possess all necessary information about the material constitutive behavior and move with the flow. They are additionally employed as integration points, whose weights are computed as the system evolves in order to ensure exact integration of the discretized conservation equations. The method is shown to achieve quadratic convergence for transient start-up flow of the Oldroyd-B fluid. In addition, we apply the method to flow of a Giesekus fluid in concentric rotating cylinders, and in flow through an abrupt 4:1 contraction, comparing favorably to available analytical, experimental, and simulation results as appropriate.