stable and fast fluid-solid coupling for incompressible...
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Stable and Fast Fluid-Solid Coupling for Incompressible SPH
Copyright of figures and other materials in the paper belongs to original authors.
Presented by MyungJin Choi
2017-09-18
Computer Graphics @ Korea University
X.Shao et al.Eurographics 2016
MyungJin Choi | 2017-09-18| # 2Computer Graphics @ Korea University
• We propose a novel stable and fast particle method to couple PCISPH and LSM
Which animates the visually realistic interaction of fluids and deformable solids allowing larger time steps or velocity differences
By combining the boundary particles with a momentum-conserving velocity-position correction scheme
• Our approach can alleviate the particle deficiency issues and prevent the penetration artefacts
• We further simulate the stable deformation and melting of solid objects based on a highly extended LSM model
• In order to improve the time performance of each time step, we entirely implement the unified particle framework on GPUs
1. Introduction
MyungJin Choi | 2017-09-18| # 3Computer Graphics @ Korea University
2. Related Work
Boundary Condition
Interaction of Fluids with Deformable Solids[Muller et al. / CASA 2004]
Direct Forcing for Lagrangian Rigid-Fluid Coupling[Becker M. et al. / TVCG 2009]
Realtime two-way coupling of meshless fluids and nonlinear FEM[Yang L. P. et al. / CGF 2012]
MyungJin Choi | 2017-09-18| # 4Computer Graphics @ Korea University
2. Related Work
Mirror Particle Method
Ghost SPH for Animating Water [Schechter H. et al. / SIGGRAPH 2012]
MyungJin Choi | 2017-09-18| # 5Computer Graphics @ Korea University
2. Related Work
Solid-Fluid Interaction (1/2)
A unified particle method for fluid-solid interactions[Solenthaler B. et al. / CAVW 2006]
A unified particle method for fluid-solid interactions[Ihmsen M. et al. / VRIPHYS 2010]
MyungJin Choi | 2017-09-18| # 6Computer Graphics @ Korea University
2. Related Work
Solid-Fluid Interaction (2/2)Versatile rigid-fluid coupling for incompressible SPH[Akinci N. et al. / TOG 2012]
Consistent surface model for SPH-based fluid transport[Orthmann J. et al. / SIGGRAPH 2013]
Coupling elastic solids with SPH fluids[Akinci N. et al. / CAVW 2013]
MyungJin Choi | 2017-09-18| # 7Computer Graphics @ Korea University
• A field quantity 𝐴𝑖 of particle 𝑖 at position 𝐗𝑖
• The density, pressure and viscosity force of fluid particle 𝑖
3. The Coupling Method
3.1 Incompressible SPH Fluid Solver (1/2)
MyungJin Choi | 2017-09-18| # 8Computer Graphics @ Korea University
• We enforce the incompressibility of SPH fluids using the promising PCISPH method
3. The Coupling Method
3.1 Incompressible SPH Fluid Solver (2/2)
MyungJin Choi | 2017-09-18| # 9Computer Graphics @ Korea University
• Our method designs a three-layered particle model
GPs(vertices of the triangle meshes) is used to render geometry
SBPs is used to calculate interaction
IBPs is used to control the deformation of objects
3. The Coupling Method
3.2 Coupling Force Computations (1/5)
Triangle mesh(left), SBPs(middle), IBPs(right)
MyungJin Choi | 2017-09-18| # 10Computer Graphics @ Korea University
• Our method designs a three-layered particle model
(1) Computing one-way density contributions of SBPs and IBPs to fluid particles
(2) Computing two-way density contributions of SBPs and fluid particles
(3) Distributing the coupling forces exerted on SBPs to neighbouring IBPs
3. The Coupling Method
3.2 Coupling Force Computations (2/5)
MyungJin Choi | 2017-09-18| # 11Computer Graphics @ Korea University
• (1) Computing one-way density contributions of SBPs and IBPs to fluid particles
When calculating the density of a fluid particles near the solid boundary, we take both neighbouring SBPs and IBPs into account
3. The Coupling Method
3.2 Coupling Force Computations (3/5)
MyungJin Choi | 2017-09-18| # 12Computer Graphics @ Korea University
• (2) Computing two-way density contributions of SBPs and fluid particles
We only consider interactions between fluid particles and SBPs
• Pressure
• Viscosity
• Interface Tension
3. The Coupling Method
3.2 Coupling Force Computations (4/5)
MyungJin Choi | 2017-09-18| # 13Computer Graphics @ Korea University
• (3) Distributing the coupling forces exerted on SBPs to neighbouring IBPs
For an IBPs particle 𝑑𝑘, the distributed coupling force is computed by:
3. The Coupling Method
3.2 Coupling Force Computations (5/5)
MyungJin Choi | 2017-09-18| # 14Computer Graphics @ Korea University
• The fluid particle is considered to penetrate the boundary at the position 𝐱𝑠𝑗 equilibrium distance of fluid particles
3. The Coupling Method
3.3 Velocity-Position Correction Scheme (1/5)
MyungJin Choi | 2017-09-18| # 15Computer Graphics @ Korea University
• For a fluid particle 𝑓𝑖 penetrating several SBPs, we propose to dynamically generate a virtual boundary particle 𝑠𝑘 colliding with it
• A filed quantity 𝐀sk of the virtual boundary particle 𝑠𝑘 is the
weighted average of the values of the neighbouring SBPs penetrated by 𝑓𝑖 𝐀sk are normal, position and velocity
3. The Coupling Method
3.3 Velocity-Position Correction Scheme (2/5)
MyungJin Choi | 2017-09-18| # 16Computer Graphics @ Korea University
• First, correct position of 𝑓𝑖 as
• The velocity of 𝑓𝑖 is corrected according to boundary material and the law of momentum conservation
Project the velocities of 𝑓𝑖 and 𝑠𝑘 to the normal and the tangential direction of 𝑠𝑘
3. The Coupling Method
3.3 Velocity-Position Correction Scheme (3/5)
MyungJin Choi | 2017-09-18| # 17Computer Graphics @ Korea University
• To enforce the non-penetration constraint at the fluid-solid interfaces, we ensure that the corrected velocity components in the normal direction of 𝑠𝑘 are equal
i.e. 𝐯𝑓𝑖
𝒏 = 𝐯𝑠𝑘𝑖
𝒏
• The normal direction
• The tangential direction
3. The Coupling Method
3.3 Velocity-Position Correction Scheme (4/5)
MyungJin Choi | 2017-09-18| # 18Computer Graphics @ Korea University
• Combining Equations (14) and (16),
• The velocity variation is distributed to the neighbouring penetrated SBPs of fluid particle 𝑓𝑖 according to
3. The Coupling Method
3.3 Velocity-Position Correction Scheme (5/5)
MyungJin Choi | 2017-09-18| # 19Computer Graphics @ Korea University
• Our fluid-solid coupling method only samples the inner of solids with lattice vertices
The inner lattice vertices work as IBPs in the coupling computation
3. The Coupling Method
3.4 Solid Deformation and Melting in the coupling (1/2)
MyungJin Choi | 2017-09-18| # 20Computer Graphics @ Korea University
• Work flow
(1) For each GP gi, we build a list of neighbouring IBPs 𝑑𝑗 in the
undeformed rest shape
(2) Implementing shape matching of IBPs in each time step
(3) The deformed position of GP gi at time 𝑡 is updated as the weighted average summation interpolation of the goal position of its neighbouring IBPs:
3. The Coupling Method
3.4 Solid Deformation and Melting in the coupling (2/2)
MyungJin Choi | 2017-09-18| # 21Computer Graphics @ Korea University
• In the pre-processing stage, for each lattice vertex particle 𝑖, a list of one-ring neighbours which share at least one lattice cell with particle 𝑖 is builded
A lattice vertex is labelled as an IBP, if it has a maximum number of 17 one-ring neighbours
Otherwise, label it as an SBP
3. The Coupling Method
3.4 Solid Deformation and Melting in the coupling (1/4)
MyungJin Choi | 2017-09-18| # 22Computer Graphics @ Korea University
• In the melting simulation, each solid particle 𝑖 need to be associated with a shape matching region ℜ𝑖 which for half-width 𝑤 contains 𝑖 and all particles reachable by traversing not more than 𝑤 lines from particle 𝑖
3. The Coupling Method
3.4 Solid Deformation and Melting in the coupling (2/4)
MyungJin Choi | 2017-09-18| # 23Computer Graphics @ Korea University
• In each time step, the melting process includes two operations
Heat diffusion
Phase transition
• Heat diffusion
In order to compute the temperature 𝑇𝑖(𝑡 + ∆𝑡) of particle 𝑖, 𝑇𝑖 is updated for each neighbouring particle by the following operation:
3. The Coupling Method
3.4 Solid Deformation and Melting in the coupling (3/4)
MyungJin Choi | 2017-09-18| # 24Computer Graphics @ Korea University
• Phase transition
3. The Coupling Method
3.4 Solid Deformation and Melting in the coupling (4/4)
MyungJin Choi | 2017-09-18| # 25Computer Graphics @ Korea University
• Algorithm Overview
4. CUDA-Based Implementation (1/5)
MyungJin Choi | 2017-09-18| # 26Computer Graphics @ Korea University
• All unchangeable physical values of particles are stored as textures
Density, pressures, positions, velocities, forces, goal positions, regions, one-ring neighbours and optimal transformations
• The physical properties of all particles are stored in the same CUDA arrays, and an additional flag value 𝐼
Fluid particle: 0, SBP: 1, ……, n, IBP: n+1, ……, 2n
n is the number of solid objects
4. CUDA-Based Implementation (2/5)
MyungJin Choi | 2017-09-18| # 27Computer Graphics @ Korea University
• To speed up the search of neighbouring particles, we launch kernels to construct a kd-tree on GPU
• For the GPU implementation of PCISPH
We first invoke one CUDA thread for each fluid particle to compute the viscosity force and the interface tension force
Then, another kernel is launched for each fluid particle tocompute the pressure and pressure force
• For the computation of the coupling forces
We launch a kernel for each fluid particle to compute the coupling force exerted on the neighbouring SBPs
Secondly, another kernel is launched for each IBP to compute the coupling forces
4. CUDA-Based Implementation (3/5)
MyungJin Choi | 2017-09-18| # 28Computer Graphics @ Korea University
• To change the topology of the melting object on GPU
In pre-processing stage, for each solid particle, we allocate an unsigned integer array 𝑎𝑟𝑟𝑎𝑦𝑁 of size 27 to store the initial indices of its one-ring neighbours
And an unsigned integer array 𝑎𝑟𝑟𝑎𝑦𝑅 of size 2𝑤 + 1 3 to store the initial indices of the particles belonging to the located region
• In each time step
First, A kernel is launched for each solid particle to update its one-ring neighbour array 𝑎𝑟𝑟𝑎𝑦𝑁 according to the phase transition of sold particles
Secondly, another kernel is launched for each region to update 𝑎𝑟𝑟𝑎𝑦𝑅
4. CUDA-Based Implementation (4/5)
MyungJin Choi | 2017-09-18| # 29Computer Graphics @ Korea University
• To render the surfaces of the melting objects and fluids represented by particles
We adopt the GPU-based interactive rendering method to define the distance field
Then triangle meshes are extracted by using the GPU accelerated marching cube technique provided by the NVIDIA CUDA example
4. CUDA-Based Implementation (5/5)
MyungJin Choi | 2017-09-18| # 30Computer Graphics @ Korea University
• Hardware
CPU: Xeon E5630
GPU: Geforce GTX 690
• Software
C++
CUDA
OpenGL
Pov-Ray
• renderer
5. Result and Discussions
MyungJin Choi | 2017-09-18| # 31Computer Graphics @ Korea University
5. Result and Discussions
5.1 Coupling Result (1/2)
MyungJin Choi | 2017-09-18| # 32Computer Graphics @ Korea University
5. Result and Discussions
5.1 Coupling Result (2/2)
MyungJin Choi | 2017-09-18| # 33Computer Graphics @ Korea University
5. Result and Discussions
5.2 Stability Analysis (1/5)
MyungJin Choi | 2017-09-18| # 34Computer Graphics @ Korea University
5. Result and Discussions
5.2 Stability Analysis (2/5)
MyungJin Choi | 2017-09-18| # 35Computer Graphics @ Korea University
5. Result and Discussions
5.2 Stability Analysis (3/5)
• Compared with the frozen method [SSP07]
The avoidance of penetration artifact
• Under larger timestep
• Under larger velocity differences
But not better than [SSP07] on physical accuracy
MyungJin Choi | 2017-09-18| # 36Computer Graphics @ Korea University
5. Result and Discussions
5.2 Stability Analysis (4/5)
MyungJin Choi | 2017-09-18| # 37Computer Graphics @ Korea University
5. Result and Discussions
5.2 Stability Analysis (5/5)
MyungJin Choi | 2017-09-18| # 38Computer Graphics @ Korea University
5. Result and Discussions
5.3 Time Performance
• Compared with the previous coupling method
Our approach takes about 30 times larger time steps
MyungJin Choi | 2017-09-18| # 39Computer Graphics @ Korea University
6. Conclusion and Future Work (1/2)
• We have proposed a stable and fast particle method to simulate the two-way interactions of physically based PCISPH fluids and geometric LSM-based deformable objects
• Strong Points
By combining the boundary particles with a momentum-conserving velocity-position correction scheme, our method has achieved both the alleviation of the particle deficiency issueand the prevention of the penetrations under larger time steps and velocity differences
To improve the time performance, we gave entirely implemented the unified particle method on GPUs
The fluid-solid coupling simulated by our method is visually plausible and stable
MyungJin Choi | 2017-09-18| # 40Computer Graphics @ Korea University
6. Conclusion and Future Work (2/2)
• Weak Points
our method is not physically completely accurate
The velocity-correction scheme cannot prevent penetrations well when the distance of boundary particles becomes larger than the support radius of boundary particles
• Future works
Capturing turbulent details
Simulating complex wetting effects