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Detail-Preserving Fluid Control

This paper introduces a novel fluid control technique that effectively preserves small-scale details during physical simulations. By decomposing the velocity field into coarse and fine components, we apply control forces only to the low-frequency part, thereby minimizing artificial viscosity and maintaining fine-scale motion, such as small eddies and droplets. Our method employs control particles to define local force fields, enhancing realism and dynamic behavior in fluid animations. The technique has been validated using two simulation models: Smoothed Particle Hydrodynamics (SPH) and the Lattice-Boltzmann Method (LBM).

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Detail-Preserving Fluid Control

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  1. Detail-Preserving Fluid Control N. Thűrey R. Keiser M. Pauly U. Rűde SCA 2006

  2. Abstract ◇ A new fluid control technique - Scale-dependent force control - Preserve small-scale fluid detail ◇ Control particles define local force fields - A physical simulation - A sequence of target shapes ◇ A multi-scale decomposition of the velocity field ◇ Small-scale detail is preserved

  3. Introduction ◇ Realism of fluids is important[CMT04] ◇ The fluid controlling for animation is also important[SY05b] ◇ Fine-scale detail such as small eddies or drops

  4. Introduction ◇ In previous method, control particles directly influence the fluid velocity field - It can cause noticeable smoothing effects ◇ To avoid this artificial viscosity, - Decompose the velocity field into coarse- and fine scale component - Only apply control forces to the low-frequency part - High-frequency components are largely unaffected - small-scale detail and turbulence are better preserved

  5. Introduction ◇ We achieve this decomposition by smoothing the velocity field using a low-pass filter ◇ Velocity control forces are computed with respect to the smoothed velocity field ◇ Scale-separated fluid control - Much better preserved - More dynamic and realistic looking simulations

  6. Related Work ◇ Our control paradigm is based on the concept of control particle, similar to [FF01] ◇ Control particles are independent of the underlying fluid model[FF01] A 3D Control Curve

  7. Related Work ◇ [REN04] present a method for the directable animation of photorealistic liquids using the particle levelset ◇ [TMPS03] presented an optimization technique to solve for the control parameters

  8. Related Work ◇ [FL04] proposed the idea of driving smoke toward target smoke density ◇ [HK04] derive potential fields from the initial distribution of smoke and target shape

  9. Related Work ◇ smoke[SY05a] and liquids[SY05b] matched the level set surface of the fluid with static or moving target shape

  10. Fluid Simulation Models ◇ We use two fluid simulation models to demonstrate our control method ◇ Smoothed Particle Hydrodynamics (SPH) ◇ The Lattice-Boltzmann Method (LBM)

  11. Smoothed Particle Hydrodynamics (SPH) ◇ As(r) : interpolation value at location r by a weighted sum of contributions from all particles ◇ j : iterates over all particles, mj : the mass of particle j ◇ rj : its postion, ρj : density of particle j ◇ Aj : the field quantity at rj ◇ W(r,h) : smoothing kernel with radius h

  12. Smoothed Particle Hydrodynamics (SPH) ◇ Numerically solving the Navier-Stokes equations

  13. The Lattice-Boltzmann Method (LBM) ◇ A grid based method ◇ Each grid cell stores a set of distribution functions ◇ The common three-dimensional LBM model D3Q19

  14. The Lattice-Boltzmann Method (LBM) Streaming ◇ Streaming  Collision  Relaxation

  15. The Lattice-Boltzmann Method (LBM) ei : nineteen grid velocitys(0~18) wi : w0=1/3, w1..6=1/18,w7..18=1/36 : physical fluid viscosity

  16. Fluid Control ◇ Generating Control Particles ◇ Controlling fluid using attraction force and velocity force ◇ Detail-Preserving Control

  17. Generating Control Particles ◇ Motion given by precomputed function [FM97, FF01] ◇ Shape given by a Mesh [JSW05] ◇ Motion from another fluid simulation - using SPH, LBM - very coarse simulation - The simulation may even run in realtime to animator

  18. Control Forces ◇ Attraction force : Force that pulls fluid towards the control particles ◇ Velocity Force : modifying the velocity of the fluid according to the flow determined by the control particles ◇ Control Particle Variables - pi : position of control particle - vi : velocity of control particle - hi : influence radius (2.5times the average distance)

  19. Attraction Force ◇ This force is scaled down when the influence region of the control particle is already covered with fluid ◇ Scale factor for attraction force

  20. Attraction Force ◇ Attraction force on a fluid element e ◇ : global contant that defines the strength of the attraction force ◇ if is negative, it will result in a repulsive force

  21. Velocity Force ◇ Velocity Force on a fluid element e ◇ v(e) : the velocity of the fluid element e ◇ : a constant that defines the influence of the velocity force

  22. Total Force ◇ Total control force fc(e) = fa(e) + fv(e) ◇ The new total force per volume f(e) = fc(e) + ff(e) ◇ ff(e) : the fluid force from the physical fluid simulation

  23. Detail-Preserving Control ◇ The velocity force lead to an averaging of the fluid velocities◇ Undesirable artificial viscosity◇ We want the natural small-scale fluid motion

  24. Detail-Preserving Control

  25. Detail-Preserving Control

  26. Detail-Preserving Control ◇ Smoothed velocity field ◇ This smoothed version of the fluid velocity replaces V(e) in Equation 7

  27. Detail-Preserving Control ◇ is low pass filtered velocity ◇ is high pass filtered velocity ◇ vp is the interpolated velocity of the control particles at a fluid element e

  28. Results and Discussion ◇ We have implemented our control algorithm for both an SPH and an LBM fluid solver ◇ Within the SPH solver, the existing acceleration structures can be used to query fluid particles in the neighborhood of a control particle ◇ For the LBM solver, control particles are rasterized to the grid

  29. Results and Discussion ◇ The simulation using LBM with a grid resolution took 142s per frame, including 4s for computing the control force ◇ These control particles are blended with 5k control particles sampled from the 3D model of the human figure

  30. Results and Discussion ◇ The control flow with detail-preservation retains small-scale fluid features ◇ The simulation was done using LBM with a 240*120*120 grid resolution which took 38s per frame on average ◇ The computation of the control forces took 2-4% of the total computation time

  31. Results and Discussion ◇ The mesh is only used to generate a sequence of control particles as described in Section 3.1 ◇ We used 266k particles for the SPH simulation which took 102s per frame including the computation of the control forces which took 14s

  32. Results and Discussion ◇ Our detail-preserving approach clearly reduces the artificial viscosity by the control forces ◇ The user can interactively adjust the parameters until the desired coarse-scale behavior of the fluid is obtained ◇ Our framework could also be used to control the deformation of elastic bodies

  33. Conclusions ◇ A detail-preserving approach for controlling fluids based on control particles◇ We solve the problem of artificial viscosity introduced by the control forces by applying these forces on the low-pass filtered velocity field ◇ Only the coarse scale flow of the fluid is modified while the natural small-scale detail is preserved, resulting in more natural looking controlled simulations

  34. References

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