|Date||Oct 01, 2021|
In this thesis, a finite difference methods for partial differential equations involving the interface is presented. Irregular domains are captured by the level-set method on Cartesian grids, and the jump condition or the boundary conditions are captured in a sharp manner by the ghost fluid method. Especially, we present sharp capturing methods for elliptic interface problem, two-phase incompressible flow, and single phase incompressible flow on irregular domains in the framework of the level-set method and the ghost fluid method. The numerical experiments supports the inference that the proposed method converges in Linfty L^inftynorms with non-trivial analytical solution and can handle pratical flow problems with irregular domains.