An adaptive level-set/square-root-conformation representation/discontinuous Galerkin method for simulating viscoelastic two-phase flow systems

A new numerical method, which is based on the coupling of adaptive mesh technique, level set (LS) method, square-root-conformation representation (SRCR) approach, and discontinuous Galerkin (DG) method within the dual splitting framework, is developed for viscoelastic two-phase flow problems. This combination has been more effective than expected. The LS method is performed to capture the moving interface due to its efficiency and simplicity when dealing with the significant interface deformations. The dual splitting scheme is applied to decouple the whole system into subequations, which circumvent the limitation of the Ladyzhenskaya-Babu & scaron;ka-Brezzi condition. The SRCR approach is employed to reconstruct the Oldroyd-B constitutive equation to solve the high Weissenberg number problem. The high-order DG method is performed for the spatial discretizations of equations to deal with the convection-dominated problems. In addition, the reinitialization method of the LS function and a simple mass correction technique are applied to guarantee the mass conservation in calculation. In this coupled method, there is no need to require reinitialization within every time step but after suitable time steps. Meanwhile, the adaptive mesh technique is implemented in the coupling procedure, which greatly improves the computational efficiency. The coupled algorithm is performed to simulate the swirling deformation flow, Rayleigh-Taylor instability and bubble rising problems. And the influences of the parameters on the rising speed and shape of bubble in viscoelastic liquid are analyzed in detail. The numerical results indicate that the coupled algorithm is effective and accurate for simulating the interface evolution problems with complex topological structure changes, and can guarantee the mass conservation property.