Efficient and conservative fluids using bidirectional mapping

In this paper, we introduce BiMocq2, an unconditionally stable, pure Eulerianbased advection scheme to efficiently preserve the advection accuracy of all physical quantities for long-term fluid simulations. Our approach is built upon the method of characteristic mapping (MCM). Instead of the costly evaluation of the temporal characteristic integral, we evolve the mapping function itself by solving an advection equation for the mappings. Dual mesh characteristics (DMC) method is adopted to more accurately update the mapping. Furthermore, to avoid visual artifacts like instant blur and temporal inconsistency introduced by re-initialization, we introduce multi-level mapping and back and forth error compensation. We conduct comprehensive 2D and 3D benchmark experiments to compare against alternative advection schemes. In particular, for the vortical flow and level set experiments, our method outperforms almost all state-of-art hybrid schemes, including FLIP, PolyPic and Particle-Level-Set, at the cost of only two Semi-Lagrangian advections. Additionally, our method does not rely on the particle-grid transfer operations, leading to a highly parallelizable pipeline. As a result, more than 45× performance acceleration can be achieved via even a straightforward porting of the code from CPU to GPU.