Lattice-Boltzmann Water Waves

Geist, Robert; Corsi, Christopher; Tessendorf, Jerry; Westall, James

doi:10.1007/978-3-642-17289-2_8

Cited by 5 publications

(3 citation statements)

References 19 publications

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“…The work of Tessendorf [2004a;2014], which discretizes a linearized Bernoulli equation, exhibits more realistic wave dispersion but still falls short of physically correct motion (as discussed in [Canabal et al 2016]). Some researchers have also introduced direct numerical simulators based on the lattice Boltzmann method (LBM) [Geist et al 2010], which requires a careful tuning of the LBM collision matrix to yield realistic wave speeds. Convolution-based approaches [Loviscach 2002;Ottosson 2011] aim to achieve the correct dispersion relation, but they must cope with the practical difficulties of large kernels occupying the entire simulation domain.…”

Section: Numerical Solutions To Partial Differential Equationsmentioning

confidence: 99%

Water surface wavelets

Jeschke¹,

Skřivan

Müller-Fischer³

et al. 2018

ACM Trans. Graph.

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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.

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Section: Numerical Solutions To Partial Differential Equationsmentioning

confidence: 99%

Water surface wavelets

Jeschke¹,

Skřivan

Müller-Fischer³

et al. 2018

ACM Trans. Graph.

View full text Add to dashboard Cite

show abstract

“…Once Ω is specified, equation 16is, essentially, the entire computational model. Starting with initial conditions, we apply (16) synchronously to all lattice sites and then generate the new wave height field at time t = t + τ by (14). Given a choice for Ω, students can begin implementation immediately.…”

Section: A 2-dimensional Wave Modelmentioning

confidence: 99%

A problem-based learning approach to GPU computing

Geist

Levine

Westall

2015

Proceedings of the Workshop on Education for High-Performance Computing

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Compared to CPUs, modern GPUs exhibit a high ratio of computing performance per watt, and so current supercomputer designs often include multiple racks of GPUs in order to achieve high teraflop counts at minimal energy cost. GPU programming is thus becoming increasingly important, and yet it remains a challenging task. This paper describes a course in GPU programming for senior undergraduates and first-year graduates that has been taught at Clemson University annually since 2010. The course uses problembased learning, with focus on a large, real-world problem, in particular, a system for parallel solution of partial differential equations. Although the system for solving PDEs is useful in its own right, the problem is used as a vehicle in which to explore design issues that face those attempting to achieve new levels of performance on SIMD architectures.

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“…Garcia et al developed LBM based fluid-structure interaction approach [18]. Geist et al developed a real-time approach for wave surface generation and attained 25 Hz for grid of size 1024 2 [19]. Geveler et al developed LBM based approach for simulating laminar flow with free fluid surface on multi-core CPU and many-core GPU processors and reported a factor of 8 speed-up on GPU code with respect to multi-threaded CPU code [20].…”

Section: Fluid-rigid Body Interaction Simulationmentioning

confidence: 99%

GPU based generation of state transition models using simulations for unmanned surface vehicle trajectory planning

Thakur

Švec

Gupta

2012

Robotics and Autonomous Systems

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This paper describes GPU based algorithms to compute state transition model for unmanned surface vehicles (USVs) using 6 degree of freedom (DOF) dynamics simulations of vehicle-wave interaction. State transition model is a key component of Markov Decision Process (MDP), which is a natural framework to formulate the problem of trajectory planning under motion uncertainty. USV trajectory planning problem is characterized by the presence of large and somewhat stochastic forces due to ocean waves, which can cause significant deviations in their motion. Feedback controllers are often employed to reject disturbances and get back on the desired trajectory. However, the motion uncertainty can be significant and must be considered in the trajectory planning to avoid collisions with the surrounding obstacles. In case of USV missions, state transition probabilities need to be generated on-board, to compute trajectory plans that can handle dynamically changing USV parameters and environment (e.g., changing boat inertia tensor due to fuel consumption, variations in damping due to changes in water density, variations in sea-state, etc.). The 6 DOF dynamics simulations reported in this paper are based on potential flow theory. We also present a model simplification algorithm based on temporal coherence and its GPU implementation to accelerate simulation computation performance. Using the techniques discussed in this paper we were able to compute state transition probabilities in less than 10 minutes. Computed transition probabilities are subsequently used in a stochastic dynamic programming based approach to solve the MDP to obtain trajectory plan. Using this approach, we are able to generate dynamically feasible trajectories for USVs that exhibit safe behaviors in high sea-states in the vicinity of static obstacles.

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Lattice-Boltzmann Water Waves

Cited by 5 publications

References 19 publications

Water surface wavelets

Water surface wavelets

A problem-based learning approach to GPU computing

GPU based generation of state transition models using simulations for unmanned surface vehicle trajectory planning

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