Conserving mass with the standard level set method to machine precision for two and three-phase flows

Resolving thin interfaces between various phases is an important consideration in numerical simulations of multiphase flows. In the standard level set method (LSM), the interface between distinct phases is represented by a continuous and differentiable signed distance function. The method is simple to implement, and accurately captures geometrical quantities such as surface normal and curvature, but it leads to spurious mass loss/gain during simulation. Over the past three decades, various fixes and extensions to the standard LSM have been proposed to address mass loss. In practice, some of these methods have not performed well, while others have complicated LSM implementation. A simple mass-preserving technique is presented in this talk for two and three-phase flows that conserves the mass of various phases while maintaining the simplicity of the original technique. Several canonical two-phase liquid-gas and three-phase liquid-gas-solid flow problems are used to demonstrate the new technique's mass-preserving property.