A Flux-Interpolated Advection Scheme for Fluid Simulation

A Flux-Interpolated Advection Scheme for Fluid Simulation

The visual Computer(Computer Graphics International 2021)

Naoyuki Hirasawa, Takashi Kanai, Ryoichi Ando

Two spheres collision. From left to right: semi-Lagrangian method with WENO6 interpolation (92% mass loss), methodof  characteristics  with  WENO6  (92.6%  mass  loss),  MacCormack  method  with  WENO6  (95.8%  mass  gain),  the  method  ofLentine et al. [32] (no mass change), our method with trilinear interpolation (6% mass loss). Grid resolution is 120×120×192for velocity, 240×240×384 for density

[preprint] [supplemental material] [code] [Springer]

Abstract: We propose a new advection scheme for fluid simulation that improves both conservation and numerical diffusion. Our work differs from previous works in that we re-formulate interpolation as cell-face flux of a vector field instantly constructed from a scalar field, rather than a per-point evaluation at back-traced positions. Our novel interpolation method enables excellent preservation of conservative quantities since the sum of flux exactly counteracts on cell faces, which eventually evaluates the boundary-flux of the whole domain. Our method can be implemented as a plug-and-play extension (or a temporary scratchpad) to the conventional semi-Lagrangian scheme; hence, our method naturally inherits all the benefits of semi-Lagrangian schemes and can be seamlessly integrated with existing fluid simulation pipelines together with other (black-boxed) solver components. We conducted numerical experiments to verify the accuracy of our scheme (conservation and the improved numerical diffusion) and compared its qualitative results with state-of-the-art advection schemes that are in heavy use in the production environment such as MacCormack and the WENO6 interpolation.