An adaptive Cartesian cut-cell/level-set method to simulate incompressible two-phase flows with embedded moving solid boundaries

► Outer-iteration solution procedure to solve two-phase flows. ► Well validated level set method based on a cut-cell approach in moving-body problems. ► Accurate prediction of hydrodynamic forces and pressure distributions on solid bodies. In this paper, a Cartesian grid method has been developed to simulate two dimensional unsteady viscous incompressible two-phase flows with embedded moving solid boundaries. The solid boundary is treated by a cut cell approach. The fluid–fluid interface is captured and treated by the level set method. A collocated finite volume method with nominally second-order accurate schemes in space is used for discretization. A pressure-free projection method is used to solve the equations governing incompressible flows. Adaptive mesh refinement is applied to efficiently deploy mesh cells of various sizes. The present method proposes an outer-iteration solution procedure to solve two-phase flows with partially submerged moving bodies and physically treats issues on newly exposed cells. Various test examples were computed and validated against previous analytical solutions, simulations, or experiments to prove the accuracy and effectiveness of the present method. We observed first-order spatial accuracy in a specific validating problem. In brief, the major contribution of the present work is the first-time announcement of a well validated level set method based on the cut-cell approach in moving-body problems.