Kim, ByungMoonLiu, YingjieLlamas, IgnacioRossignac, JarekPierre Poulin and Eric Galin2014-01-272014-01-2720053-905673-29-01816-0867https://doi.org/10.2312/NPH/NPH05/051-056Back and Forth Error Compensation and Correction (BFECC) was recently developed for interface computation by using the level set method. We show that it can be applied to reduce dissipation and diffusion encountered in various advection steps in uid simulation such as velocity, smoke density and image advections. BFECC can be implemented easily on top of the r st order upwinding or semi-Lagrangian integration of advection equations, while providing second order accuracy both in space and time. When applied to level set evolution, BFECC reduces volume loss signi cantly . We combine these techniques with variable density projection and show that they yield a realistic animations of two-phase ows. We demonstrate the bene ts of this approach on the image advection and on the simulation of smoke, of bubbles in water, and of a highly dynamic interaction between water, a solid, and air.