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Mode-Splitting for Highly Detail, Interactive Liquid Simulation H. Cords University of Rostock Presenter: Truong Xuan Quang

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Content 0. Abstract 1.Introduction 2. Related work 3. Our Approach 4. Implement and Result

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Abstract A new technique for highly detailed interactive liquid simulation Separated low-frequency (LF) and high-frequency (HF) LF: free surface wave, 2D wave equation HF: liquid follow, 3D Navier-Stock equation Rendering in 2.5 D Simulation liquid follow according to gravity, ground, obstacles and interaction with impacts, moving impact, etc

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Introduction Real-time liquid simulation can be classified as follows: Empirical (expert) surface simulation Physically-based surface simulation (wave equation) Physically-based volume simulation (Navier-Stokes equations )

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Introduction The Goal : mode-splitting to increase quality of the simulate liquid. Moving obstacles, rain, surface wave generation, etc…… Splitting based: Navier-Stockes based method: Fluid flow, movement of free surface 2D wave equation: fast solve wave equation Finally combines the advantages of both physically-based approaches Limitation: not valid in splashing or breaking wave

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Related work Simulation and rendering liquids and effected (e.g. [Carlson et al. 2004] [Hong and Kim 2005] [Guendelman et al. 2005] [Muller et al. 2005]). The Navier-Stokes equations are usually solved with particle-based systems (e.g Smoothed Particle Hydrodynamics - SPH), [Adabala and Manohar 2002]. In [Stam and Fiume 1995] the first real-time approach using SPH is presented. Interactive simulation of fluids was introduced in [Stam 1999] Execution on the GPU with reasonable frame rates [Harris- 2005] Solving the wave equation was presented [Yuksel et al. 2007] And etc..

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Our Approach Goal for simulation: real-time and large scale Lagrangian methods few particles Liquid volume Small grid size (Eulerain) Propose model-slitting method to simulate highly detailed surface: described by 2D wave equation is solve by FDM and liquid flow by Navier- Stockes equations there is solve with the (SPH)

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Our Approach

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For visualization we use a height field-based rendering approach most liquid surface can be rendered appropriately as height fields. However, complex liquid phenomena, such as breaking waves or splashes, cannot be visualized as height fields.

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Mode Splitting Using oceanography the method is used to simulated high frequency waves is external gravity waves-included by tide and atmospheric pressure, water waves, free surface water. And low frequency waves Internal gravity wave included by wind and density gradients, vertical turbulences. Different algorithms are used, external and internal algorithms are solved separately with different time steps c : speed of light l :amplify frequency Nth mode

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Mode Splitting Moving external waves need to be solved at small time steps The slow moving internal waves are more expensive to solve (due to complex turbulences), large time step can be used We used the 2D equation for surface simulation and a 3D SPH-based Navier-Stokes equations solver for volume flow simulation

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Surface simulation The general wave equation describes the propagations of wave in time t and space x, liquid surface wave the 2D Wave equation can be used, describing the circular wave Propagation Laplace operator in 2D and c is the velocity at the which wave propagate across The wave equation can be solved with Eulerian finite difference approach

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Implicit different method α is constant, m>0 is integer and time step size k>0, with h=l/m for each i=0, 1…, m

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Implicit different method

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Several radius wave propagations 2. Rain-Drop 3. A swimming object is moving

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Liquid simulation Navier-Stokes equations Conservation of mass (continuity equation ) in rest position V is velocity filed Ρ the pressure field μ: viscosity f: external force Incompressible liquids, density is constant Resulting in the mass conservation

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Simple and fast handling of boundary conditions as collisions Mass conservation is guaranteed (number of particles = const; mass of each particle = const) Nonlinear convective acceleration can be neglected SPH for real-time simulation

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SPH SPH (Smooth Particle Hydro-dynamics) is an simulation method for particle systems defined at discrete particle locations can be evaluated everywhere in the space. Continuous field quantities distributed in the local neighborhood according to the discrete particle positions and the smoothing kernels Wh(x). Scalar quantities A(x) can be estimated for n particles as :

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SPH Pressure force External force Viscosity force neglected Smoothing kernel for pressure and viscosity

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SPH a(t0) v(t0) xi(t0) a(t0+Δt) v(t0+ Δt) xi(t0+ Δt) The liquid volume is discredited by particles yi xi zi

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SPH

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Collisions Collisions of liquids particles with objects are using a force vector field surrounding collision objects Where d is the closet distance between object and particle n Object is normal vector of the object at the points closet object F col : is acting on each particle being close to collision objects V : reflect velocity, friction coefficient

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Free surface Extraction Generated height surface: number of neighbors potential Φ for n particles with position xi (i=1..n) is determined by the following spherical potential These particles can be detected according to their actual number of neighbors Threshold (condition of the smoothness), to reduce unwanted surface ripples cause by the discrete sampling of the liquids

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Free surface Extraction (2/2) Depending kinetic energy n particles vi velocities mi mass (i=1..m) If E kin exceeds a defined of threshold, no smoothing occurs Else bellow threshold, the number of smoothing steps is increased, until the Maximum number of smoothing step is reach

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Simulation time-steps Surface simulation (wave equation) and volume simulation (SPH) should be synchronized be integer fraction N time of WE-TS N-S TS Example of time step (TS) Synchronization, Ntime=3 WE is solved 3 times, while Navier-Stockes is solve once

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Combine surface and volume simulation Final surface just depends on the different field resolution SPH generated surface Xsph x Ysph Wave equation surface size XWE x YWE

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Rendering (1/2) Using cube map contain the environment for approximating the effects. Surface variation (position and normal) calculating reflection and refraction vectors. Reflection and refraction is described by Fresnel equation.

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Rendering (2/2) Planar light map is generated via light ray tracing using Snell’s law Other liquid can be also applied, simple liquid like: milk, cola, oil. SPH WE

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4.1 Implementation and Results Using OpenGL 2.0 and shading language GLSL in C++, dual core PC 2.6 GHz AMD Athlon 64 CPU. 2 GBs of RAM and graphics card ATIRadeon x 1900 GPU. Using Parallel implementation with one core simulation SPH and one core solving wave equation

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4.1 Implementation and Results Performance of the technique mainly depend on the following parameter: Number of SPH particles X SPH. Y SPH X WE. Y WE Results of experiments show that SPH simulation account for 40-70% of the run time-less than 4000 particles. Disadvantage is impossible to visualize 3D liquid effects like: splashes, breaking waves, cause by 2.5D rendering approach (2D WE + 3D SPH+ rendering)=2.5D

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4.1 Implementation and Results Advantaged: Volume interaction (moving glass of water, obstacles) Surface interaction (rain, moving objects) Automatic, natural and global flow Object moving with the follow Simulation pool or sea

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4.2 Conclusion and future work Simulation of the low frequency liquid flow and the high frequency free surface waves are separated 2D WE and 3D fluid (SPH-method) presented realistic and highly detailed results Future works: Simulation in real-time environments at high frame rates, better rendering approach. GPU or PPU (Physic Processing Unit) for physical calculations. Applied for larger liquid volume

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