A Robust, Fully Adaptive Hybrid Level-Set/Front-Tracking Method for Two-Phase Flows with an Accurate Surface Tension Computation (Communications in Computational Physics, 2010)
We present a variable time step, fully adaptive in space, hybrid method forthe accurate simulation of incompressible two-phase flows in the presence of surfacetension in two dimensions. The method is based on the hybrid level set/front-trackingapproach proposed in [H. D. Ceniceros and A. M. Roma, J. Comput. Phys., 205, 391-400, 2005]. Geometric, interfacial quantities are computed from front-tracking via theimmersed-boundary setting while the signed distance (level set) function, which isevaluated fast and to machine precision, is used as a fluid indicator. The surface tensionforce is obtained by employing the mixed Eulerian/Lagrangian representationintroduced in [S. Shin, S. I. Abdel-Khalik, V. Daru and D. Juric, J. Comput. Phys., 203,493-516, 2005] whose success for greatly reducing parasitic currents has been demonstrated.The use of our accurate fluid indicator together with effective Lagrangianmarker control enhance this parasitic current reduction by several orders of magnitude.To resolve accurately and efficiently sharp gradients and salient flow features weemploy dynamic, adaptive mesh refinements. This spatial adaption is used in concertwith a dynamic control of the distribution of the Lagrangian nodes along the fluid interfaceand a variable time step, linearly implicit time integration scheme. We presentnumerical examples designed to test the capabilities and performance of the proposedapproach as well as three applications: the long-time evolution of a fluid interface undergoingRayleigh-Taylor instability, an example of bubble ascending dynamics, anda drop impacting on a free interface whose dynamics we compare with both existingnumerical and experimental data.