Water surface wavelets

Abstract

obstacles in real time while simultaneously preserving minute details and accommodating very large simulation domains.Previous methods for simulating 2D water waves directly compute the change in height of the water surface, a strategy which imposes limitations based on the CFL condition (fast moving waves require small time steps) and Nyquist's limit (small wave details require closely-spaced simulation variables). This paper proposes a novel wavelet transformation that discretizes the liquid motion in terms of amplitude-like functions that vary over space, frequency, and direction, effectively generalizing Fourier-based methods to handle local interactions. Because these new variables change much more slowly over space than the original water height function, our change of variables drastically reduces the limitations of the CFL condition and Nyquist limit, allowing us to simulate highly detailed water waves at very large visual resolutions. Our discretization is amenable to fast summation and easy to parallelize. We also present basic extensions like pre-computed wave paths and two-way solid fluid coupling. Finally, we argue that our discretization provides a convenient set of variables for artistic manipulation, which we illustrate with a novel wave-painting interface. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike International 4.0 License. 94:2 • Jeschke et al.

Physics-Based Simulation of Ocean Scenes in Marine Simulator Visual System

“…Kass and Miller adopted the shallow water equation [42], which is a simplified form of the full Navier-Stokes equations, to model the waves. Jeschke et al [43] proposed a model coupling spectrum-based approach and PDE method together, which improved the interaction of moving obstacles and reduced the limitations of the CFL condition and Nyquist limit. These simplified methods sacrifice the ability to simulate arbitrary fluid motion, and have many limitations in dealing with complex interactive scenes.…”

Fundamental solutions for water wave animation

“…Irving et al [Irving et al 2006] also propose to improve the performance of 3d fluid simulation with 2d techniques by coarsening the simulation grid with tall cells away from the free surface interface. Recently, Jeschke et al [2018] proposed a wavelet approach that convects a wavelet amplitude function on a grid. Their method can represent high frequency wave details even with a coarse grid, but their method sacrifices the ability to accurately keep track of coherent wave phases or reproduce common interference patterns.…”

“…This paper presents new strategies for efficiently animating water surface waves, especially for simulation in large, open domains with abundant high-frequency visual details and detailed boundaries. Such scenarios are particularly challenging for the state of the art in computer animation, which either rely on finite-difference approximations [Tessendorf 2004a], require a grid or mesh for the entire domain [Jeschke et al 2018;Jeschke and Wojtan 2015], or require Lagrangian wave samples to fill the domain wherever details are present [Jeschke and Wojtan 2017;Yuksel et al 2007]. Many of these approaches become prohibitively expensive for open (practically infinite) domains with extremely high-frequency capillary ripples.…”

An optimization on water wave diffraction approximation based on wave packets

“…Nonetheless, these approaches are sensitive to the CFL condition and the Nyquist's limit. Recently, Jeschke et al proposed an approach for diminishing the effect of Nyquist's limit via carrying out a simulation on a lower resolution instead of visualized resolution through a novel Gabor transformation. As stated in the work of Jeschke and Wojtan, compared to particle‐based approaches, artificial damping is often needed to keep stability in grid‐based approaches.…”

“…As a boundary element method, it has several advantages compared to the currently generally used finite element method. 11,19,20 Firstly, instead of discretizing the whole region as in the finite element method, the boundary element method only needs to discretize the boundary, which reduces the dimension of the problem by one, thus simplifying the solution procedures and improves computational efficiency. Besides, under the same discrete precision conditions, the accuracy of the boundary element method is higher than that of the finite element method.…”