  Adaptive interface-Mesh un-Refinement (AiMuR) based Sharp-Interface
Level-Set-Method (SI-LSM) is proposed for both uniform and non-uniform
Cartesian-Grid. The AiMuR involves interface location based dynamic
un-refinement (with merging of the four control volumes) of the Cartesian grid
away from the interface. The un-refinement is proposed for the interface solver
only. A detailed numerical methodology is presented for the AiMuR and
ghost-fluid method based SI-LSM. Advantage of the novel as compared to the
traditional SI-LSM is demonstrated with a detailed qualitative as well as
quantitative performance study, involving the SI-LSMs on both coarse grid and
fine grid, for three sufficiently different two-phase flow problems: dam break,
breakup of a liquid jet and drop coalescence. A superior performance of AiMuR
based SI-LSM is demonstrated - the AiMuR on a coarser non-uniform grid
($NU_{c}^{AiMuR}$) is almost as accurate as the traditional SI-LSM on a uniform
fine grid ($U_{f}$) and takes a computational time almost same as that by the
traditional SI-LSM on a uniform coarse grid ($U_{c}$). The AMuR is different
from the existing Adaptive Mesh Refinement (AMR) as the former involves only
mesh un-refinement while the later involves both refinement and un-refinement
of the mesh. Moreover, the proposed computational development is significant
since the present adaptive un-refinement strategy is much simpler to implement
as compared to that for the commonly used adaptive refinement strategies. The
proposed numerical development can be extended to various other multi-physics,
multi-disciplinary and multi-scale problems involving interfaces.
