Contents Contents Fluid - PowerPoint PPT Presentation

Physics-based Fluid Simulations for Computer Graphics Ryoichi Ando ＣＧ物理ベース流体シミュレーション安東遼一

Contents

Contents Fluid Solver

Contents Fluid Solver Surface Tracker

Contents Fluid Solver Surface Tracker FLIP Solver

• Ph.D student @ Kyushu Univ • Visiting Scientist at IST Austria • Fluid Simulations • SIGRRAPH 2013 Tech. paper with Chris Wojtan and Nils Thuerey Short Bio

Fluid Solver Surface Tracker FLIP Solver

Fluid Solver

Navier-Stokes Equations s.t.

Navier-Stokes Equations s.t. How velocity changes over time

Navier-Stokes Equations s.t. How velocity changes over time Advection term

Navier-Stokes Equations s.t. How velocity changes over time Advection term Pressure term

Navier-Stokes Equations s.t. How velocity changes over time Advection term Pressure term Viscosity term

Navier-Stokes Equations s.t. How velocity changes over time Advection term Pressure term Viscosity term External force term

Navier-Stokes Equations s.t. How velocity changes over time Advection term Pressure term Viscosity term Incompressiblity Constraint External force term

Navier-Stokes Equations

Navier-Stokes Equations Large Matrix

Navier-Stokes Equations Large Matrix p u = RHS

Navier-Stokes Equations Large Matrix p u = RHS Newton Iterations...

Operator Splitting

Operator Splitting [Stable fluid, Stam99]

First-order integration

First-order integration e.g, advection

First-order integration e.g, advection First-order accuracy!

Simulation Steps

Simulation Steps Advection term

Simulation Steps Advection term Pressure term

Simulation Steps Advection term Pressure term Viscosity term

Simulation Steps Advection term Pressure term Viscosity term External force term

Simulation Steps Advection term Pressure term

Simulation Steps Advection term Pressure term Simulation Loop...

Advection term Pressure term

Advection term

Advection term Computing

Advection term Computing Scalar Scalar

Advection term Computing Expand... Scalar Scalar

Advection term Computing Expand... Key component ! Scalar Scalar

Advection term Computing Velocity field Scalar field

Advection term Computing Velocity field Scalar field Ground Truth

Advection term Computing How to discretize ?

Advection term Computing

Advection term Computing Central Difference

Advection term Computing Central Difference Accurate

Advection term Computing Central Difference

Advection term Computing Upwind Scheme If If

Advection term Computing High-order Upwind Scheme ( WENO5 )

Advection term Computing High-order Upwind Scheme ( WENO5 ) Upwind Scheme

Advection term Pressure term

Pressure term

Computing Pressure term

Computing Pressure term Pressure Poisson Equation

Pressure term Pressure Poisson Equation Boundary Conditions of

Pressure term Discretizing

Pressure term Discretizing Divergence Theorem

Pressure term Discretizing MAC Grid

Pressure term Discretizing 1 2 3 4 p

Pressure term Discretizing Solid wall

Pressure term Discretizing Solid wall 1 2 =

Pressure term Discretizing Empty Matrix

Pressure term Discretizing p u* =

Pressure term Discretizing p u* = (Semi-)Positive Definite System

Contents Contents Fluid - PowerPoint PPT Presentation

Physics-based Fluid Simulations for Computer Graphics Ryoichi Ando Contents Contents Fluid Solver Contents Fluid Solver Surface Tracker Contents Fluid Solver Surface

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