Particle-based fluid simulation for interactive applications

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Presentation transcript:

Particle-based fluid simulation for interactive applications Matthias Müller David Charypar Markus Gross 9557501 陳岳澤

Outline Introduction Navier-Stokes Equation SPH (Smoothed Particle Hydrodynamics ) Smooth Kernel Marching Cubes Result

Introduction Navier-Stokes Equation describe the motion of fluid substances such as liquids and gases Use Smoothed Particle Hydrodynamics (SPH) to simulate fluids with free surfaces. Interactive simulation (about 5 fps).

Navier-Stokes Equation -1 Conservation of momentum equation Three components: Pressure term External force term Viscosity term v: velocity, : density, p: pressure, g: external force, : viscosity coefficient

Navier-Stokes Equation -2 The acceleration ai of particle i is (fi is body force) Using ai , we can get velocity and position of particle i

SPH -1 Originally developed for astrophysical problems (1977). Interpolation method for particles. Properties that are defined at discrete particles can be evaluated anywhere in space. Uses smoothing kernels to distribute quantities.

SPH -2 Smoothing of attribute A mj: mass rj : density Aj: quantity to be interpolated W: smoothing kernel h

Particle density Smoothing of attribute A Particle density

Pressure Term Navier-Stokes Equation Pressure Term

Viscosity term Navier-Stokes Equation Viscosity Term

External force term Other external forces are directly applied to the particles. Collisions: In case of collision the normal component of the velocity is flipped.

Smoothing Kernel -1 Has an impact on the stability and speed of the simulation. ex: Avoid square-roots for distance computation. Sample smoothing kernel:

Smoothing Kernel -2 all points inside a radius of ‘h’ are considered for “smoothing”. Thick line: the kernel Thin line: the gradient of kernel Dashed line: the laplacian of kernel

Smoothing Kernel -3 For n particles n2 potential interactions! To reduce to linear complexity O(n2) define interaction cutoff distance h

Smoothing Kernel -4 Fill particles into grid with spacing h Only search potential neighbors in adjacent cells

Marching Cubes -1 To visualize the free surface

Marching Cubes -2

Result Interactive Simulation (5fps) Marching Cubs 2200 particle Point Splatting