An conservative anti-diffusion technique for the level set method

A novel conservative level set method is introduced for the approximation of two-phase incompressible fluid flows. The method builds on recent conservative level set approaches and utilizes an entropy production to construct a balanced artificial diffusion and artificial anti-diffusion. The method is self-tuning, maximum principle preserving, suitable for unstructured meshes, and neither re-initialization of the level set function nor reconstruction of the interface is needed for long-time simulation. Computational results in one, two and three dimensions are presented for finite element and finite volume implementations of the method.