Advections with Significantly Reduced Dissipation and Diffusion

Back and Forth Error Compensation and Correction (BFECC) was recently developed for interface computation using a level set method. We show that BFECC can be applied to reduce dissipation and diffusion encountered in a variety of advection steps, such as velocity, smoke density, and image advections on uniform and adaptive grids and on a triangulated surface. BFECC can be implemented trivially as a small modification of the first-order upwind or semi-Lagrangian integration of advection equations. It provides second-order accuracy in both space and time. When applied to level set evolution, BFECC reduces volume loss significantly. We demonstrate the benefits of this approach on image advection and on the simulation of smoke, bubbles in water, and the highly dynamic interaction between water, a solid, and air. We also apply BFECC to dye advection to visualize vector fields.