Stable and Fast Fluid-Solid Coupling for Incompressible...

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


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]


2. Related Work

Mirror Particle Method

Ghost SPH for Animating Water [Schechter H. et al. / SIGGRAPH 2012]


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]


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]


• 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)


• We enforce the incompressibility of SPH fluids using the promising PCISPH method


3.1 Incompressible SPH Fluid Solver (2/2)


• 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


3.2 Coupling Force Computations (1/5)

Triangle mesh(left), SBPs(middle), IBPs(right)


• 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




• (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




• (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) Distributing the coupling forces exerted on SBPs to neighbouring IBPs

For an IBPs particle 𝑑𝑘, the distributed coupling force is computed by:




• The fluid particle is considered to penetrate the boundary at the position 𝐱𝑠𝑗 equilibrium distance of fluid particles


3.3 Velocity-Position Correction Scheme (1/5)


• 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




• 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




• 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




• Combining Equations (14) and (16),

• The velocity variation is distributed to the neighbouring penetrated SBPs of fluid particle 𝑓𝑖 according to




• 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


3.4 Solid Deformation and Melting in the coupling (1/2)


• 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:




• 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




• 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




• 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:




• Phase transition




• Algorithm Overview

4. CUDA-Based Implementation (1/5)


• 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



• 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



• 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



• 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



• Hardware

CPU: Xeon E5630

GPU: Geforce GTX 690

• Software

C++

CUDA

OpenGL

Pov-Ray

• renderer

5. Result and Discussions



5.1 Coupling Result (1/2)



5.1 Coupling Result (2/2)



5.2 Stability Analysis (1/5)




• 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



5.3 Time Performance

• Compared with the previous coupling method

Our approach takes about 30 times larger time steps


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


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

Stable and Fast Fluid-Solid Coupling for Incompressible...

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