Solving phase appearance/disappearance two-phase flow problems with high resolution staggered grid and fully implicit schemes by the Jacobian-free Newton-Krylov Method

The phase appearance/disappearance issue presents serious numerical challenges in two-phase flow simulations. Although many existing nuclear reactor safety analysis codes use different kinds of treatments for the phase appearance/disappearance problem, there are no fully consensual solutions. In this paper, a high-resolution spatial discretization scheme on staggered grid mesh and fully implicit time integration methods was used in two-phase flow simulations. Numerical treatments of the momentum equations were introduced for the disappearing phase without the need to use a cut-off value on void fraction. A discretized nonlinear system was solved using the Jacobian-free Newton Krylov (JFNK) method, which does not require expensive and error-prone derivation and implementation of analytical Jacobian matrix. These methods were tested with several two-phase flow problems with phase appearance/disappearance phenomena considered, such as a linear advection problem, an oscillating manometer problem, and a sedimentation problem. The combined methods demonstrated extremely robust and stable behaviors in solving the one-dimensional two-phase flow problems with phase appearance/disappearance. High-resolution spatial discretization and second-order fully implicit method also demonstrated their capabilities in significantly reducing numerical errors.