Reducing numerical dissipation in smoke simulation

Numerical dissipation acts as artificial viscosity to make smoke viscous. Reducing numerical dissipation is able to recover visual details smeared out by the numerical dissipation. Great efforts have been devoted to suppress the numerical dissipation in smoke simulation in the past few years. In this paper we investigate methods of combating the numerical dis-sipation. We describe visual consequences of the numerical dissipation and explore sources that introduce the numerical dissipation into course of smoke simulation. Methods are investigated from various aspects including grid variation, high-order advection, sub-grid compensation, invariant conservation, and particle-based improvement, followed by discussion and comparison in terms of visual quality, computational overhead, ease of implementation, adaptivity, and scalability, which leads to their different applicability to various application scenarios. Smoke is desirable in visual effect and video game industries. It is also one of challenging problems in computer graphics due to its complexity and turbulence. To obtain realistic smoke and gaseous phenomena, physically based methods with Navier–Stoke Equations (NSEs) have been explored to model underlying fluid dynamics. Although numerically integrating NSEs have been studied in computational fluid dynamics (CFD), computer graphics researches focus on simplified discretization and numerical schemes when visual quality matters most. Simplifications make physically based methods possible for smoke simulation but introduce the numerical dissipation. The numerical dissipation increases fluid viscosity to make it appear more viscous than intended. It degrades the visual appearance by smearing out fine details and damping down the motion quickly. The numerical dissipation has been recognized to have substantial visual consequences to the smoke simulation. Many sources introduce numerical dissipation to the course of the smoke simulation. Coarse spatiotemporal dis-cretization produces numerical truncation errors, which is proven to have a form of viscosity [1]. As fluid quantities are only defined on discrete locations such as grid points and particles, interpolation schemes are required to calculate values at undefined positions, which is equivalent to smoothing operations that produce the numerical dissipa-tion. The semi-Lagrangian method [2] is widely used for the smoke simulation attributed to its unconditional stability and ease of implementation, but it generates a large amount of the numerical dissipation in backward tracing and advection subroutines. Many advanced methods are constructed based on the semi-Lagrangian method to guarantee the unconditional stability. However, they also inherit the disadvantage of massive numerical dissipation.