Covector fluids

Nabizadeh, Mohammad Sina; Wang, Stephanie; Ramamoorthi, Ravi; Chern, Albert

doi:10.1145/3528223.3530120

Cited by 14 publications

(29 citation statements)

References 52 publications

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“…The Stable Fluids method [Stam 1999] yields a significant amount of numerical viscosity causing the results to appear blurred and damped. Researchers have addressed this artifact with error correction schemes [Kim et al 2006;Selle et al 2008], higher-order interpolation [Losasso et al 2006b;Nave et al 2009], improved backtracking schemes [Cho et al 2018;Jameson et al 1981], particle-based advection [Fu et al 2017;Jiang et al 2015;Zhu and Bridson 2005], energy-preserving integration, [Mullen et al 2009], a posteriori vorticity correction [Fedkiw et al 2001;, reflection [Narain et al 2019;Strang 1968;Zehnder et al 2018] and Lie advection [Nabizadeh et al 2022]. Flow map methods offer another alternative option, as elaborated below.…”

Section: Fluid Simulationmentioning

confidence: 99%

“…Qu et al [2019] trade off accuracy for efficiency by advecting the backward map in a semi-Lagrangian-like manner; and bring in the forward map to realize the BFECC error compensation [Kim et al 2006]. Nabizadeh et al [2022] effectively combine bidirectional flow maps with impulse-based fluid dynamics [Buttke 1992;Feng et al 2022;Oseledets 1989], using the mappings along with their Jacobians to perform circulation-preserving advection.…”

Section: Fluid Simulationmentioning

confidence: 99%

“…Since the four flow map quantities: 𝜙, 𝜓 , F and T can fully prescribe material transport, they can serve as essential ingredients for accurate fluid simulations. To illustrate, we consider the impulse form of the Euler equations for inviscid flow [Cortez 1995;Feng et al 2022;Nabizadeh et al 2022]:…”

Section: Physical Model 31 Mathematical Foundationmentioning

confidence: 99%

“…A flow map-based solver for Equation 5 is introduced to the graphics community by Nabizadeh et al [2022], which solves the equation by first computing the backward flow map 𝜓 and its Jacobian T , and then reconstructing the impulse 𝒎 by evaluating:…”

Section: Physical Model 31 Mathematical Foundationmentioning

confidence: 99%

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Fluid Simulation on Neural Flow Maps

Deng,

Yu,

Zhang

et al. 2023

ACM Trans. Graph.

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We introduce Neural Flow Maps, a novel simulation method bridging the emerging paradigm of implicit neural representations with fluid simulation based on the theory of flow maps, to achieve state-of-the-art simulation of in-viscid fluid phenomena. We devise a novel hybrid neural field representation, Spatially Sparse Neural Fields (SSNF), which fuses small neural networks with a pyramid of overlapping, multi-resolution, and spatially sparse grids, to compactly represent long-term spatiotemporal velocity fields at high accuracy. With this neural velocity buffer in hand, we compute long-term, bidirectional flow maps and their Jacobians in a mechanistically symmetric manner, to facilitate drastic accuracy improvement over existing solutions. These long-range, bidirectional flow maps enable high advection accuracy with low dissipation, which in turn facilitates high-fidelity incompressible flow simulations that manifest intricate vortical structures. We demonstrate the efficacy of our neural fluid simulation in a variety of challenging simulation scenarios, including leapfrogging vortices, colliding vortices, vortex reconnections, as well as vortex generation from moving obstacles and density differences. Our examples show increased performance over existing methods in terms of energy conservation, visual complexity, adherence to experimental observations, and preservation of detailed vortical structures.

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Section: Fluid Simulationmentioning

confidence: 99%

Section: Fluid Simulationmentioning

confidence: 99%

Section: Physical Model 31 Mathematical Foundationmentioning

confidence: 99%

Section: Physical Model 31 Mathematical Foundationmentioning

confidence: 99%

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Fluid Simulation on Neural Flow Maps

Deng,

Yu,

Zhang

et al. 2023

ACM Trans. Graph.

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“…From the Helmholtz vorticity laws, the surfaces are material surfaces for all t ≥ 0 in Euler flows. Therefore, solving the spin Euler equation (2.7) is similar to a vortex method (Yang et al 2021;Nabizadeh et al 2022;Xiong et al 2022) for simulating ideal flows. Since the primary variable s of (2.7) has unit length, the fixed magnitude of s can avoid the numerical blowup arising from numerical instabilities.…”

Section: Introduction To the Spin Euler Equationmentioning

confidence: 99%

Lagrangian dynamics and regularity of the spin Euler equation

Meng,

Yang

2024

J. Fluid Mech.

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We derive the spin Euler equation for ideal flows by applying the spherical Clebsch mapping. This equation is based on the spin vector, a unit vector field encoding vortex lines, instead of the velocity. The spin Euler equation enables a feasible Lagrangian study of fluid dynamics, as the isosurface of a spin-vector component is a vortex surface and material surface in ideal flows. We establish a non-blowup criterion for the spin Euler equation, suggesting that the Laplacian of the spin vector must diverge if the solution forms a singularity at some finite time. The direct numerical simulations (DNS) of three ideal flows – the vortex knot, the vortex link and the modified Taylor–Green flow – are conducted by solving the spin Euler equation. The evolution of the Lagrangian vortex surface illustrates that the regions with large vorticity are rapidly stretched into spiral sheets. The DNS result exhibits a pronounced double-exponential growth of the maximum norm of Laplacian of the spin vector, showing no evidence of the finite-time singularity formation if the double-exponential growth holds at later times. Moreover, the present criterion with Lagrangian nature appears to be more sensitive than the Beale–Kato–Majda criterion in detecting the flows that are incapable of producing finite-time singularities.

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Physics-based fluid simulation in computer graphics: Survey, research trends, and challenges

Wang,

Xu,

Liu

et al. 2024

Comp. Visual Media

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Physics-based fluid simulation has played an increasingly important role in the computer graphics community. Recent methods in this area have greatly improved the generation of complex visual effects and its computational efficiency. Novel techniques have emerged to deal with complex boundaries, multiphase fluids, gas–liquid interfaces, and fine details. The parallel use of machine learning, image processing, and fluid control technologies has brought many interesting and novel research perspectives. In this survey, we provide an introduction to theoretical concepts underpinning physics-based fluid simulation and their practical implementation, with the aim for it to serve as a guide for both newcomers and seasoned researchers to explore the field of physics-based fluid simulation, with a focus on developments in the last decade. Driven by the distribution of recent publications in the field, we structure our survey to cover physical background; discretization approaches; computational methods that address scalability; fluid interactions with other materials and interfaces; and methods for expressive aspects of surface detail and control. From a practical perspective, we give an overview of existing implementations available for the above methods.

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Covector fluids

Cited by 14 publications

References 52 publications

Fluid Simulation on Neural Flow Maps

Fluid Simulation on Neural Flow Maps

Lagrangian dynamics and regularity of the spin Euler equation

Physics-based fluid simulation in computer graphics: Survey, research trends, and challenges

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