We develop a unified adaptive level set (LS) framework using the multi-level collocated grid for incompressible two-phase flows. This framework allows us to advance all variables level by level using either the subcycling or the non-subcycling method such that the data advancement on each level is fully decoupled. A series of synchronization operations are designed to keep the momentum and mass conserved across all levels. A multi-level re-initialization method for the LS function is also proposed, which greatly improves the mass conservation of the two-phase flows. The collocated grid allows the use of a single set of differential schemes and interpolation operations for all variables, which greatly simplifies the numerical implementation. The capability and robustness of the computational framework are validated by a variety of canonical problems, including the inviscid shear layer, gravity wave, rising bubble, and Rayleigh-Taylor instability. It is shown that the present multi-level scheme can accurately resolve the interfaces of the two-phase flows with gravitational and surface tension effects while having good momentum and energy conservation. At last, a three-dimensional dam breaking problem is simulated to show the efficiency and significant speedup of the proposed framework.
Bibliographical noteFunding Information:
Y. Z., A. X., and L. S. gratefully acknowledge the support to this work by the Office of Naval Research ( N00014-17-1-2658 and N00014-19-1-2139 ) and National Science Foundation ( OCE-1924799 ) on this work. Y. Z. would also like to gratefully thank the researchers in the Lawrence Berkeley National Lab (LBNL) for the discussions about the synchronization algorithms.
© 2021 Elsevier Inc.
- Adaptive mesh refinement (AMR)
- Level set
- Two-phase flow