A narrow-band gradient-augmented level set method for multiphase incompressible flow

A finite-difference based numerical method for the simulation of multiphase incompressible flows is presented. The proposed algorithm adapts the gradient-augmented level set method of Nave et al. [25] for use in multiphase fluid simulations by interpolating the fluid velocity and introducing a simple reinitialization procedure. The method is carried out only along a narrow band surrounding the interface, reducing computational effort while preserving the advantages of the gradient-augmented method. Numerical results show excellent agreement with an analytical solution and available experimental data. A new experimental benchmark is introduced, using data gathered in a wedge-driven wave tank. In addition to the optimally local advection scheme and sub-grid resolution afforded by the new method, numerical comparisons with the standard level set method reveal superior volume conservation.