Closest point turbulence for liquid surfaces

Abstract

and NILS THÜREY Scanline VFXWe propose a method of increasing the apparent spatial resolution of an existing liquid simulation. Previous approaches to this "up-resing" problem have focused on increasing the turbulence of the underlying velocity field. Motivated by measurements in the free surface turbulence literature, we observe that past certain frequencies, it is sufficient to perform a wave simulation directly on the liquid surface, and construct a reduced-dimensional surface-only simulation. We sidestep the considerable problem of generating a surface parameterization by employing an embedding technique known as the Closest Point Method (CPM) that operates directly on a 3D extension field. The CPM requires 3D operators, and we show that for surface operators with no natural 3D generalization, it is possible to construct a viable operator using the inverse Abel transform. We additionally propose a fast, frozen core closest point transform, and an advection method for the extension field that reduces smearing considerably. Finally, we propose two turbulence coupling methods that seed the high-resolution wave simulation in visually expected regions.

Ocean surface approximation from scattered numerical marine forecast data

“…By adopting this method, heights data can be modified within a frame. To further improve the performance, Thuerey et al [10], [11] developed a 3D iWave kernel and produced visually indistinguishable results. For large scale visualization of numerical marine forecast data, the shallow river turbulent technique is apparently no easy to copy with the situation.…”

A Semi‐Lagrangian Closest Point Method for Deforming Surfaces

“…While most existing techniques consider only static surfaces, in some recent works it was raised the importance of solving PDEs on deforming surfaces. A practical example can be found in the context of fluid simulation, where free boundary surfaces resulting from coarse simulations are enriched in a post‐process by high‐frequency details [KTT13]. These details are either to costly to be simulated in 3D or they cannot be captured by the underlying physical model.…”

“…On one side of the spectrum there are purely Eulerian methods, based on a sampling that remains fixed in the three‐dimensional embedding space. These techniques often employ implicit surface representations and provide a very natural coupling to fully three‐dimensional Eulerian simulations [KTT13]. On the other side there are purely Lagrangian methods, employing a dynamic sampling that follows the surface movement and the evolution of the simulated properties on the surface at the same time.…”

“…Building upon the work of Hong, Auer, Kim and co‐workers [HZQW10, AMT*12, KTT13], we contribute a semi‐Lagrangian closest point method (SLCPM) for the interactive simulation of fluid effects on deforming surfaces. This method has some beneficial properties for up‐resing.…”

“…Our technique can overcome some major restrictions and limitations of previous techniques which have applied the CPM to deforming surfaces. While the method by Hong et al [HZQW10] requires an additional level‐set representation of the surface on which the 2D simulation is carried out, Kim et al [KTT13] relies on the existence of an external velocity field in which MacCormack advection can be performed.…”