Post on 28-Jul-2020
Filament-based realistic turbulent wake synthesis
Xiangyun Liao et al.CASA 2017
Copyright of figures and other materials in the paper belong to original authors.
Presented by Man-Ki Hong
2017. 10. 19
Computer Graphics @ Korea University
Man-Ki Hong | 2017. 10. 19 | # 2Computer Graphics @ Korea University
• Turbulent wake is turbulence that forms behind obstacles as fluid flow passes through them.
Ex) Boat driving on the ocean
Introduction
Man-Ki Hong | 2017. 10. 19 | # 3Computer Graphics @ Korea University
• In this paper, we propose a vortex filament-based turbulent wake synthesis method for realistically simulating the liquid turbulent wake with ring-shaped vortical structures and obtaining natural diffusion effects of turbulent wake.
We propose a vortex filament-based method to generate turbulent wake for liquid with ring-shaped structures. Ourmethod samples vortex filaments at the separation points on arbitrary obstacle and emits these filaments into the liquid flow.
To enhance the liquid turbulent wake details, we introduce the surface tension model to the liquid turbulent wake synthesis, adding the anticurvature effects of the surface tension to achieve natural turbulent wake diffusion effects.
Introduction
Man-Ki Hong | 2017. 10. 19 | # 4Computer Graphics @ Korea University
• “Stable Fluids”[Stam J. /Proceedings of the 26th AnnualConference on Computer Graphicsand Interactive Techniques 1999]
• “Visual simulation of smoke” [Fedkiw R et al. /Proceedings of the 28th AnnualConference on Computer Graphicsand Interactive Techniques 2001]
Related Work
Eulerian grid-based methods
Man-Ki Hong | 2017. 10. 19 | # 5Computer Graphics @ Korea University
• “Vortex Fluid for Gaseous Phenomena”[Sang Il Park et al./Proceedings of the 2005 ACMSIGGRAPH/ Eurographics Symposiumon Computer Animation]
• “Realistic and stable simulation ofturbulent details behind objects insmoothed-particle hydrodynamicsfluids”[Shao X et al./ CAVW 2015]
Related Work
Vortex Particles Method
Man-Ki Hong | 2017. 10. 19 | # 6Computer Graphics @ Korea University
• “Lagrangian vortex sheets for animating fluids”[Pfaff T et al. / ACM TOG 2012]
Related Work
Vortex Sheet Method
Man-Ki Hong | 2017. 10. 19 | # 7Computer Graphics @ Korea University
• “Simulation of smoke based on vortex filamentprimitives”[Angelidis A et al. / Proceedings of the 2005 ACM SIGGRAPH/Eurographics Symposium on ComputerAnimation]
• “Smoke rings from smoke”[Weißmann S et al. / ACM TOG 2014]
Related Work
Vortex Filament Method
Man-Ki Hong | 2017. 10. 19 | # 8Computer Graphics @ Korea University
• Vortex filament, denoted as 𝛾, is a basic Lagrangian primitive to represent vorticity in fluids
• The vortex filament induces circularmotion around the filament curvetangent based on a circulationnumber 𝛤
Vortex Filament Method
Man-Ki Hong | 2017. 10. 19 | # 9Computer Graphics @ Korea University
• In physics, Helmholtz’s theorems tell us that
(a) The circulation of a vortex filament is constant along its length
(b) A vortex filament cannot end in a fluid
• it must extend to the boundaries of the fluid or form a closed path.
(c) In the absence of rotational external forces, a fluid that is initially irrotational remains irrotational.
• The theorem is formulated as follows :
Vortex Filament Method
Man-Ki Hong | 2017. 10. 19 | # 10Computer Graphics @ Korea University
• This method is based on the WCSPH
SPH summary
physical quantity
neighbor particles
weight : inverse proportion to the distance between i and j
m : mass𝜌 : density
Man-Ki Hong | 2017. 10. 19 | # 11Computer Graphics @ Korea University
Filament-Based Turbulent Wake Synthesis
Method Overview
Man-Ki Hong | 2017. 10. 19 | # 12Computer Graphics @ Korea University
• We adopt the method of Akinci et al. for fluid-obstacle coupling.
“Versatile rigid-fluid coupling for incompressible SPH”ACM TOG 2012
• We sample filament on the separation point when the SPH fluids pass by the obstacle.
• The separation point is defined by the Reynolds number.
Filament-Based Turbulent Wake Synthesis
Filament Sampling
Man-Ki Hong | 2017. 10. 19 | # 13Computer Graphics @ Korea University
• A dimensionless quantity that can assess the fluid motion on the boundary of obstacles.
• It distinguish fluid flow that is laminar flow or turbulent flow
Filament Sampling
Reynolds Number
Man-Ki Hong | 2017. 10. 19 | # 14Computer Graphics @ Korea University
• For each sampled boundary particles, we define the corresponding local Reynolds number as follows:
Filament Sampling
Reynolds Number
𝜌𝑖 and 𝐯𝑖 : mean density and mean velocity of fluid particles
inside the support domain of boundary particle 𝑖 with radius ℎ.
𝑳𝑖 : Characteristic linear dimension of the obstacles at boundary
particle 𝑖.
𝜇 : viscosity of the fluid
• For the boundary particle 𝑖, when 𝑅𝑒𝑖 > 𝑅𝑒0 , we define it as
the separation point.
Man-Ki Hong | 2017. 10. 19 | # 15Computer Graphics @ Korea University
• We selected the boundary particles whose distances to the plane 𝛼𝑠 are less than 𝑑0 as well as under plane 𝛽 as the filament vertices.
denoted as 𝑷 = {𝑝1, 𝑝2, … , 𝑝𝑛𝑠}
Filament Sampling
Filament Vertices
𝐯0 : initial relative velocity for fluid passing by the obstacle
𝑠 : found separation point on the obstacle surface
𝛼𝑠 : plane that is perpendicular to the 𝐯0
𝛽 : horizontal plane at the highest fluid-free surface particle in plane 𝛼𝑠
Man-Ki Hong | 2017. 10. 19 | # 16Computer Graphics @ Korea University
• Note that the obstacle may not entirely be under the horizontal plane 𝛽
• We define the following function to disable or enable theimpact of each filament segment :
Filament Sampling
Impact of The Filament Segment
Man-Ki Hong | 2017. 10. 19 | # 17Computer Graphics @ Korea University
• The vorticity of the vortex filament vertex at separation point 𝑠can be calculated with its nearest SPH fluid particle 𝑗 using the inverted Biot–Savart integration:
Filament Sampling
Vorticity & Circulation
𝐝𝑠𝑗 : vector from 𝑗 to 𝑠
𝐧𝑠 : vertex normal of 𝑠
𝐯𝑗 : velocity of 𝑗
𝑉𝑠 : volume of 𝑠, 𝑉𝑠 = 𝑚𝑠/𝜌𝑠 = 𝑚𝑠/( 𝑘 𝑚𝑘𝑊𝑘), (𝑘 : boundary particle neighbors)
• The initial circulation Γ𝑖 of the sampled filament 𝛾𝑖 at the separation point 𝑠 can be calculated by the following equation:
Man-Ki Hong | 2017. 10. 19 | # 18Computer Graphics @ Korea University
• The vorticity field of the fluid is concentrated on a finite collection of vortex filaments 𝛾, and then the generated velocity field reduces to a sum of line integrals along the filaments:
Turbulent Wake Synthesis
Velocity Field
𝑚 : the number of filaments
𝛤𝑖 : circulation of the sampled filament 𝛾𝑖
𝛾𝑖(𝑡) : parameterization of the filament line
𝛾𝑖′(𝑡) : tangent of the filament curve
Man-Ki Hong | 2017. 10. 19 | # 19Computer Graphics @ Korea University
• To effectively synthesize turbulent wake, here, we define a turbulent wake formation region as a cuboid 𝐶𝑣 with length 𝐿𝑐
behind the obstacle
Turbulent Wake Synthesis
Turbulent Wake Formation Region
• Once the filament is advected out of the turbulent wake formation region, it will be removed.
Man-Ki Hong | 2017. 10. 19 | # 20Computer Graphics @ Korea University
• For each fluid particle 𝒌 in the turbulent wake formation region, its velocity can be approximated by the following :
Turbulent Wake Synthesis
Compute Velocity
𝐭𝑗
𝝉𝑗
𝐯𝑘(𝐱)
𝑝𝑗
𝑝𝑗+1
𝐱 : position of 𝑘
𝑚 : the number of sampled filaments
𝑛𝑖 : the vertices’ number of filament 𝛾𝑖
𝜏𝑗 : (𝑝𝑗 + 𝑝𝑗+1)/2
𝐭𝑗 : 𝑝𝑗𝑝𝑗+1
Man-Ki Hong | 2017. 10. 19 | # 21Computer Graphics @ Korea University
• The turbulent wake may appeal unnatural with large curvature because of the absence of surface tension.
• We use color function 𝑐 to compute the location and characteristics of the liquid-air interface on which the surface force will apply.
Turbulent Wake Enhancement
Color Field
• The surface particles set 𝐵 can be detected with a threshold parameter 𝑙0, 𝐵 = 𝑖 ||𝛻𝑐|| > 𝑙0}.
• The normal direction 𝐧 from liquid to air can be computed from the gradient of color field 𝐧 = 𝛻𝑐.
Man-Ki Hong | 2017. 10. 19 | # 22Computer Graphics @ Korea University
• The final surface tension term in the momentum equation is
where 𝜎 is the surface tension coefficient.
Turbulent Wake Enhancement
Surface Tension
• We use the normalized form of the SPH divergence which is suited for nonfull supported fields as it restores first orderconsistency
Man-Ki Hong | 2017. 10. 19 | # 23Computer Graphics @ Korea University
Implementation
Man-Ki Hong | 2017. 10. 19 | # 24Computer Graphics @ Korea University
• To validate the performance of our method, we simulate the liquid turbulent wake in scenarios with static and moving obstacles, and compare our method with the WCSPH, the vortex particle method and our method without surface tension.
• The experimental platform includes :
Intel(R) Core(TM) i5-3470S CPU @ 2.9GGHz, 8GB memory, Geforce GTX 660M
• We set
𝜇 = 1.0, 𝑅𝑒0 = 2,500, 𝐿𝑑 = 0.6, 𝐿𝑐 = 15, ℎ = 0.5, 𝑓 = 5, 𝑑 = 3.
Results
Environment
Man-Ki Hong | 2017. 10. 19 | # 25Computer Graphics @ Korea University
Results
Video
Man-Ki Hong | 2017. 10. 19 | # 26Computer Graphics @ Korea University
Results
Performance Comparison
Man-Ki Hong | 2017. 10. 19 | # 27Computer Graphics @ Korea University
• The main limitation of our method is that the parameters need to be manually tuned for better turbulent wake synthesis results.
• In future work, we are to investigate the adaptive parameters selection method for achieving more robust simulation.
• In addition, we also plan to incorporate the foam and bubble simulation into our method for generating liquid turbulent wake with more appealing free-surface rendering and realistic visual details.
Conclusion And Future Work