An improved interface preserving level set method for simulating three dimensional rising bubble

A new interface preserving level set method is developed in three steps to simulate bubble rising problems. In the first step of the solution algorithm, the level set function ϕ is advected by a pure advection equation. An intermediate step is performed to obtain new level set function through an improved smoothed Heaviside function. To keep the new level set function as a distance function and to conserve mass bounded by the interface, in the final solution step a mass correction term is added to the re-initialization equation. This two-phase numerical model is developed underlying the projection method to compute the incompressible Navier-Stokes solutions in collocated grids. In the discretizations of the level set advection equation and the re-initialization equation, the fifth-order weighted essentially non-oscillatory scheme is applied to prevent numerical oscillations occurring around discontinuous interface. The performance of the proposed level set method in conserving mass is compared with conventional level set method applied to solve the single bubble rising problem and the bubble bursting problem at a free surface. Merger of two bubbles is also investigated. Numerical results show that not only the surface tension force can be accurately calculated but also the mass can be conserved excellently using the present level set method.