A conservative local interface sharpening scheme for the constrained interpolation profile method

A conservative local interface sharpening scheme has been developed for the constrained interpolation profile method with the conservative semi‐Lagrangian scheme, because the conservative semi‐Lagrangian scheme does not feature a mechanism to control the interface thickness, thus causing an increase of numerical error with the advance of the time step. The proposed sharpening scheme is based on the conservative level set method proposed by Olsson and Kreiss. However, because their method can cause excessive deformation of the free‐surface in certain circumstances, we propose an improvement of the method by developing a local sharpening technique. Several advection tests are presented to assess the correctness of the advection and the improved interface sharpening scheme. This is followed by the validations of dam‐breaking flow and the rising bubble flows. The mass of the fluid is exactly conserved and the computed terminal velocity of the rising bubble agrees well with the experiments compared with other numerical methods such as the volume of fluid method (VOF), the front tracking method, and the level set method. Copyright © 2011 John Wiley & Sons, Ltd.