Seung-wook Kim, Kiwon Um
Producing vivid fluid details, such as the sharp spatial structure of inter-
faces and vortices, is essential for high-quality fluid simulations in computer
graphics. The advection solver is a vital component of fluid simulation,
and the semi-Lagrangian method is widely adopted as a central building
block for many advanced advection methods thanks to its unconditional
stability. Despite these notable improvements, the numerical dissipation
and energy loss inherent in conventional linear interpolation remain con-
siderable drawbacks, compromising visual fidelity. This paper proposes a
novel extension of the core semi-Lagrangian advection algorithm to signifi-
cantly alleviate numerical dissipation and energy loss. Our extension uses
a dimension-splitting weighted sum with a windowed sinc (also known as
Lanczos) kernel, leveraging the properties of the sinc function to construct
a bounded, near-orthogonal semi-Lagrangian reconstruction. Our experi-
ments, comparing various advection methods and their discrete operators,
demonstrate that our extension significantly improves the orthogonality of
the operator, energy-retaining behavior and enables richer visual details.
Lanczos Advection: Near-Orthogonal Semi-Lagrangian Reconstruction for Fluid Simulation