A Robust Lattice Boltzmann Method for Simulations of Viscoelastic Two-Phase Flows

Simulation of multiphase viscoelastic flows involves various challenges including the need to do interfacial tracking and computing the fluid motions that are coupled with nonlinear polymeric viscoelastic stresses (VES). The solution approaches are subject to numerical stability issues under large contrasts in timescales of the VES and the fluid motions, and due to large stiffness at high density ratios of the fluids. We discuss robust l lattice Boltzmann (LB) methods using central moments and multiple relaxation times for computing the VES based on the Oldoryd-B model, the two-fluid motions, and the interface tracking represented by the Allen-Cahn phase field model. The stability issues with the solution of VES are addressed via a locally implicit approach using a L-stable and second order accurate composite trapezoidal rule and the backward difference formula (TR-BDF2) through Strang splitting. The stiffness issues at high density ratios are alleviated via the use of a transformation of the distribution function for the fluid motions based on the pressure rather than density and performing collisions in terms of their central moments. We present various case studies involving the motion of bubbles and drops in viscoelastic fluids to show the utility of our approach.