Filament-based realistic turbulent wake...

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


• 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


• “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


• “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


• “Lagrangian vortex sheets for animating fluids”[Pfaff T et al. / ACM TOG 2012]

Related Work

Vortex Sheet Method


• “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


• 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



• 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 :



• 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


Filament-Based Turbulent Wake Synthesis

Method Overview


• 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


• 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


• 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.


• 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


• 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


• 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:


• 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


• 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 Formation Region

• Once the filament is advected out of the turbulent wake formation region, it will be removed.


• For each fluid particle 𝒌 in the turbulent wake formation region, its velocity can be approximated by the following :


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


• 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.


• 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


Implementation


• 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


Results

Video


Results

Performance Comparison


• 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

Filament-based realistic turbulent wake...

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