# Particle-Based Fluid Simulation. CSE169: Computer Animation Steve Rotenberg UCSD, Spring 2016

Size: px
Start display at page:

Download "Particle-Based Fluid Simulation. CSE169: Computer Animation Steve Rotenberg UCSD, Spring 2016"

Transcription

1 Particle-Based Fluid Simulation CSE169: Computer Animation Steve Rotenberg UCSD, Spring 2016

2 Del Operations Del: = x Gradient: s = s x y s y z s z Divergence: v = v x + v y + v z x y z Curl: v = v z v y y z v x v z z x v y v x x y Laplacian: 2 s = 2 s x s y s z 2

3 Transport Equations Advection: Convection: ds dt dv dt = v s = v v Diffusion: Viscosity: Pressure: ds dt = k 2 s dv dt = μ 2 v dv dt = p

4 Navier-Stokes Equation The incompressible Navier-Stokes equation describes the forces on a fluid as the sum of convection, viscosity, and pressure terms: v t = v v + μ 2 v p In addition, we also have the incompressibility constraint: v = 0 As discussed in the previous lecture, these are formulated from the point of view of a fixed point in space (Eulerian frame of reference)

5 Lagrangian Approach In the Lagrangian approach, we formulate the Navier-Stokes equation from the point of view of a particle moving along with the fluid The pressure and viscosity terms don t change, but the convection term goes away entirely dv dt = μ 2 v p The paper also adds a term for externally applied forces as well as a 1 ρ term to account for the fact that the particle based methods will have some variation in density dv i dt = μ 2 v i 1 ρ i p i + f i m i

6 Particle-Based Fluids

7 Grid-Based Methods Fluid dynamics has traditionally been simulated on uniform grids or irregular meshes These techniques are good for engineering applications due to their potential for high accuracy They are effective in computer graphics uses as well, particularly for smoke and simulations of airflows However, it is very difficult to handle fluid interfaces (such as the water-air boundary) and complex splashing situations, which are the situations one often wants in entertainment applications

8 Smooth Particle Hydrodynamics Particle based fluid simulation is often referred to as smooth particle hydrodynamics or SPH Some of the original work was done for simulating galactic gas dynamics by astrophysicists The technique was introduced to the computer graphics community around 2003 In recent years, advances in the techniques as well as increases in GPU computational power have made large-scale SPH simulations possible The technique has proven very effective, especially for simulating very dynamic situations with lots of splashing and interaction with complex surfaces

9 SPH Fluids in Computer Graphics We will follow the paper SPH Fluids in Computer Graphics Authors: Markus Ihmsen, Jens Orthmann, Barbara Solenthaler, Andreas Kolb, Matthias Teschner This was a State of The Art Report (STAR) published in Eurographics 2014, and it summarizes much of the development on the subject that had been done in the previous 10 years This is a great overview of the subject and the important issues, and with lots of other great references in the bibliography Many of the formulas in these slides come from the paper as well as a few quoted statements

10 Field Representation We saw that scalar and vector fields can be represented by grids or meshes by sampling the field at the grid points and interpolating the values in between Alternately can use a meshless set of irregularly spaced particles to represent a field Rather than being a 0 dimensional point, a particle is thought of as being smeared out over some small radius The maximum radius of influence for a particle is called the support radius The particles have to be close enough together so that they effectively cover all of the domain of interest, and often they are arranged so that every point in the domain is overlapped by several particles (maybe around 3-10)

11 Field Representation Each particle i represents a small sample of the fluid so it will have a mass m i, position x i, and velocity v i We will also compute various properties per particle such as the local density ρ i, pressure p i, or volume V i

12 Kernel Function We define a kernel function W() that represents the strength of a particle s influence as a function of the distance from the particle At the support radius, we expect W() to go to 0 and smoothly increase to 1 as we get closer to the particle There have been many kernel functions proposed, and we will look at the one used in the paper

13 Kernel Function A quantity A i at arbitrary position x i is approximately computed with a set of known quantities A j at neighboring particle positions x j A i = j m j ρ j A j W ij With W ij being a kernel function of the form W ij = W x i x j h = W q = 1 f q hd A typical choice for the function f () would be f q = 3 2π 2 3 q q q q < q 2

14 Kernel Function W ij = W x i x j h = W q = 1 f q hd The value d is the number of dimensions The value h is the smoothing radius, which is not the same as the support radius The particle spacing is typically close to h From examining the equations, one can see that the support radius is 2h in the example from the paper, but they mention it may vary from h to 3h depending on choice of kernel function f()

15 Derivative Computation When using uniform grids, we were able to easily compute various spatial derivatives by using finite differencing With particles, the irregular spacing makes derivative computation a little more tricky and several approaches have been used in the literature The paper uses the following: A i = ρ i m j A i ρ i 2 + A j j ρ j 2 W ij A i = 1 ρ i j m j A ij W ij 2 A i = 2 j m j ρ j A ij x ij W ij x ij x ij h 2

16 Derivative Computation Notice that all of the derivatives involve summing over j, which is the set of nearby particles within the support radius In order to do the calculations, every particle must determine which particles are nearby This can be problematic when you are dealing with millions of particles, and so special data structures are required to make this neighbor search fast We will look at those in a little bit

17 Equations of Motion SPH uses the Lagrangian form of the Navier-Stokes equation: dv i dt = μ 2 v i 1 ρ i p i + f i m i This is computed for each particle and then integrated using the standard forward Euler method of integration that we ve been using for other particle systems Note that it requires a density ρ and pressure p to be calculated first and the paper has a couple different methods to do that depending on the specific approach

18 Algorithm The paper presents 4 different algorithms for SPH simulation They are all similar and effectively try to calculate the same thing, but they use different computational approaches and don t produce the exact same results The main difference between the approaches involves the exact order that things are done and how the incompressibility constraint is handled Most methods allow for some compression, but some of the better approaches attempt to enforce incompressibility using iterative approaches or solutions to large systems of equations In general, the more sophisticated methods require more time to compute a single time step, but run more stable and can handle larger time steps The result is that usually the more sophisticated approaches will outperform the simpler approaches in real world use cases

19 Integration & Time Steps We need small time steps to keep things stable, but ideally we could use larger time steps if things aren t moving as quickly We can therefore consider adapting the time step over time based on what is happening in the simulation It is common to base this off of the Courant-Friedrich- Levy (CFL) condition that limits the time step so that the fastest particle doesn t move more than some portion of it s smoothing radius: t λ v h max with λ 0.4

20 Spatial Hash Tables

21 Neighbor Search The physics equations per particle are relatively fast to compute, as they mainly involve multiplication and addition with very little division, no trig functions, and no real exponentials One of the most expensive parts of the physics simulation in SPH is actually the search for the nearest neighbors for each particle To calculate the derivatives, every particle needs to know which particles are within its support radius If there are N particles, and every particle could potentially be a neighbor to every other particle, the search is inherently O N 2 which gets extremely expensive as N gets high (which it will!) With the right choice of data structures however, we can reduce the neighbor search for a single particle to constant time, making the overall search linear or O N

22 Uniform Grids We could use a grid structure to optimize our neighbor search by storing a list of particles in each grid cell The spacing of the grid cells is set to the support radius of the particles so that all of a particles neighbors will be within one grid cell away To search for neighbors, each particle would loop through the 3x3x3 set of nearby cells The physics will limit the maximum number of particles per cell with the pressure force Therefore, the neighbor search for a single particle is constant, as it requires checking 27 cells that will each contain roughly the same number of particles The two big problems with grids is the fact that they have a limited size, putting a range on how far our particles can move, and that they take up a lot of memory to account for all of the unoccupied cells. If we try to increase the range our particles can move, we need to increase the grid size, causing a very large memory penalty

23 Spatial Hash Table A spatial hash table is a wonderful data structure that has all of the advantages of uniform grids and doesn t suffer from the memory or range limitations It is effectively a virtual grid that extends infinitely in every direction, but we only store data for occupied cells, making unoccupied cells totally free

24 Spatial Hash Table A spatial hash table operates very much like a standard hash table, where a hashing function maps some key (like a string) to an integer, which is then mod ed into an array of slots. Items can be added, removed, or accessed through the table in constant time The spatial hash table is essentially the same thing, but it uses a 3D position to map to a grid cell which is then hashed into the table The table stores occupied cells, each of which may contain several particles, but will be limited to some maximum number due to the physics If more than one occupied cell maps to the same table entry, then the table entry can simply contain a linked list of cells. In practice, if the table size is anywhere near the number of particles, then this will happen very rarely The paper refers to a compact hashing scheme that uses some additional tricks to keep the memory size manageable

25 Hash Function A point in infinite space is mapped into a finite list of cells using a hash function such as: c = x d p 1 xor y d p 2 xor z d p 3 %m With d being the cell spacing, m the hash table size, and p 1, p 2, and p 3 being large prime numbers such as , , and

26 Rendering

27 SPH Rendering Now that we can simulate water with SPH and can do the calculations efficiently, we turn to the subject of rendering Rendering a smooth surface from a set of particles is challenging, and one of the more common criticisms of the technique is its inability to handle calm smooth water surfaces But who wants to simulate calm smooth water surfaces anyway? Actually, modern surface extraction techniques do a pretty good job at this, but one can still often spot bumpy visual artefacts in SPH renderings The paper describes 4 overall approaches to rendering SPH simulations: Extract a polygonal surface and render that through standard techniques Render each surface particle individually as some kind of splat Use a screen-space technique to render the pixels the contain the water surface Use a volumetric rendering technique Surface extraction is more common for high quality renderings, and splat based and screen-space techniques tend to be more appropriate for real time rendering

28 Marching Cubes Most surface extraction techniques are based on the marching cubes algorithm or some variation of it With this approach, we first create a virtual grid around our particles where the grid size is a little smaller than the particle radius We then evaluate a distance or density type function on this grid, where each point computes some density value based on the particle nearby The surface is implicitly defined as being the set of points where the density value is some constant (i.e., an isosurface). An isosurface is a 3D version of the 2D isocurves one finds on a topographic map To find the surface, we loop through each cell and examine the 8 values on the corners of the cell. If some of the values of the cell are above the isosurface value and some are below, then we know that the surface passes through the cell. We then triangulate that small section of the surface and repeat for all cells

29 Marching Cubes

30 Marching Cubes

31 Marching Cubes In this example, we use marching cubes to triangulate the water-air interface. One can get good results by using a sufficiently high resolution and using a very carefully designed distance/density function, referred to in the paper However, marching cubes is a very powerful technique for visualizing 3D fields of all sorts. It is used throughout scientific visualization to view all things such as electromagnetic fields, quantum wave functions, gravitational fields, stress fields, MRI scan data, and more

32 SPH Extensions

33 SPH Extensions Surface tension: There are some good models for surface tension that can be added to the force computation. These will improve the behavior of small scale phenomena such as sheet breakup, and spherical drop formation Two-scale simulation: A common extension to SPH is to do a two level simulation where the first (course) level has does a full physics simulation on a smaller number of particles (say 500,000) and then the second (fine) level simply advects a large number of surface particles (maybe 5 million) through the velocity field calculated from the course scale. This allows efficient physics computation plus high visual detail at the surface where it is needed Adaptive particles: It s nice to have lots of small particles in areas where we need them such as around splashes. However, for slower moving areas of the fluid, it is inefficient to use tons of tiny particles. Adaptive schemes use particles of varying sizes that adapt automatically to the flow complexity. In other words, they will use large particles where the flow is smooth and the large particles will automatically subdivide into smaller particles as things get more dynamic. Likewise, small particles will coalesce into bigger particles where the flow slows down. Note that this applies to purely the physical simulation of the particles, and so this method is different, yet compatible with the two-scale method described above

34 SPH Extensions Foam, spray, & bubbles: One can also support special particles to represent foam on the water surface, spray of fine scale droplets in the air, and air bubbles under the surface. These particles are created in places where there are violent interactions between water particles near the air-water surface. This method dramatically improves the visual quality of crashing waves and large splashing scenes Interaction with solids, cloth: water particles can interact with solid objects like dynamic rigid bodies, or deformable elastic bodies such as cloth. A common approach is to create a bunch of virtual particles along the surface of the solid objects that interact with the water particles just like any other particle. The forces applied to the virtual particles are passed through to the rigid or elastic bodies to allow for two-way interaction between fluids and solids High viscosity: when we increase the fluid viscosity substantially, the fluid starts to behave more and more like a solid. When combined with non-newtonian viscosity, we can get fluids that can hold a solid shape such as clay or toothpaste

35 SPH Extensions Solid mechanics: if we take high viscosity to an extreme, we can actually model deformable solid objects as well, such as rubber, metals, and more. Behaviors such as elasticity, plasticity, and fracture can be included Phase changes: if we can model both liquids and solids with SPH, then we can model phase changes such as melting, freezing, boiling, and condensation Granular materials: SPH has been extended to handle physics of granular materials like sand. Sand moves in a very fluid way, but requires some additional static friction behaviors that allow it to form piles. Also, as with water, one can use two-scale techniques where sand it modeled at a course level and then rendered at a finer scale

36 Project 5

37 Project 5 Choose one of the following: Inverse Kinematics: implement a single chain of 5 or more links that can interactively track a goal position that the user can move around in x, y, and z SPH: implement the basic SPH simulation algorithm with a small number of particles (say 1000 or less). No hash tables or surface extraction is required, but the particles should render as individual spheres or sprites at least Rigid Body Dynamics: implement the basic rigid body motion equations (Newton- Euler) for a box and implement collisions with the ground plane Locomotion: implement a 4 or 6 legged walking creature that uses analytical IK for the legs and supports at least two different gaits Quaternion Interpolation: implement a tool that allows the user to manually rotate at least 5 boxes and then displays a moving box that uses smooth quaternion interpolation to pass through the different boxes Choose Your Own: if you have an idea you d like to do for the project, that would be great, but please come talk to me about it first

### CGT 581 G Fluids. Overview. Some terms. Some terms

CGT 581 G Fluids Bedřich Beneš, Ph.D. Purdue University Department of Computer Graphics Technology Overview Some terms Incompressible Navier-Stokes Boundary conditions Lagrange vs. Euler Eulerian approaches

### 2.7 Cloth Animation. Jacobs University Visualization and Computer Graphics Lab : Advanced Graphics - Chapter 2 123

2.7 Cloth Animation 320491: Advanced Graphics - Chapter 2 123 Example: Cloth draping Image Michael Kass 320491: Advanced Graphics - Chapter 2 124 Cloth using mass-spring model Network of masses and springs

### Interaction of Fluid Simulation Based on PhysX Physics Engine. Huibai Wang, Jianfei Wan, Fengquan Zhang

4th International Conference on Sensors, Measurement and Intelligent Materials (ICSMIM 2015) Interaction of Fluid Simulation Based on PhysX Physics Engine Huibai Wang, Jianfei Wan, Fengquan Zhang College

### Fluid Simulation. [Thürey 10] [Pfaff 10] [Chentanez 11]

Fluid Simulation [Thürey 10] [Pfaff 10] [Chentanez 11] 1 Computational Fluid Dynamics 3 Graphics Why don t we just take existing models from CFD for Computer Graphics applications? 4 Graphics Why don t

### Particle-based Fluid Simulation

Simulation in Computer Graphics Particle-based Fluid Simulation Matthias Teschner Computer Science Department University of Freiburg Application (with Pixar) 10 million fluid + 4 million rigid particles,

### Realtime Water Simulation on GPU. Nuttapong Chentanez NVIDIA Research

1 Realtime Water Simulation on GPU Nuttapong Chentanez NVIDIA Research 2 3 Overview Approaches to realtime water simulation Hybrid shallow water solver + particles Hybrid 3D tall cell water solver + particles

### Navier-Stokes & Flow Simulation

Last Time? Navier-Stokes & Flow Simulation Optional Reading for Last Time: Spring-Mass Systems Numerical Integration (Euler, Midpoint, Runge-Kutta) Modeling string, hair, & cloth HW2: Cloth & Fluid Simulation

### CS-184: Computer Graphics Lecture #21: Fluid Simulation II

CS-184: Computer Graphics Lecture #21: Fluid Simulation II Rahul Narain University of California, Berkeley Nov. 18 19, 2013 Grid-based fluid simulation Recap: Eulerian viewpoint Grid is fixed, fluid moves

### Realistic Animation of Fluids

1 Realistic Animation of Fluids Nick Foster and Dimitris Metaxas Presented by Alex Liberman April 19, 2005 2 Previous Work Used non physics-based methods (mostly in 2D) Hard to simulate effects that rely

### CS 231. Fluid simulation

CS 231 Fluid simulation Why Simulate Fluids? Feature film special effects Computer games Medicine (e.g. blood flow in heart) Because it s fun Fluid Simulation Called Computational Fluid Dynamics (CFD)

### SPH: Why and what for?

SPH: Why and what for? 4 th SPHERIC training day David Le Touzé, Fluid Mechanics Laboratory, Ecole Centrale de Nantes / CNRS SPH What for and why? How it works? Why not for everything? Duality of SPH SPH

### Fluids in Games. Jim Van Verth Insomniac Games

Fluids in Games Jim Van Verth Insomniac Games www.insomniacgames.com jim@essentialmath.com Introductory Bits General summary with some details Not a fluids expert Theory and examples What is a Fluid? Deformable

### Water. Notes. Free surface. Boundary conditions. This week: extend our 3D flow solver to full 3D water We need to add two things:

Notes Added a 2D cross-section viewer for assignment 6 Not great, but an alternative if the full 3d viewer isn t working for you Warning about the formulas in Fedkiw, Stam, and Jensen - maybe not right

### Navier-Stokes & Flow Simulation

Last Time? Navier-Stokes & Flow Simulation Pop Worksheet! Teams of 2. Hand in to Jeramey after we discuss. Sketch the first few frames of a 2D explicit Euler mass-spring simulation for a 2x3 cloth network

### Lagrangian methods and Smoothed Particle Hydrodynamics (SPH) Computation in Astrophysics Seminar (Spring 2006) L. J. Dursi

Lagrangian methods and Smoothed Particle Hydrodynamics (SPH) Eulerian Grid Methods The methods covered so far in this course use an Eulerian grid: Prescribed coordinates In `lab frame' Fluid elements flow

### Realistic Animation of Fluids

Realistic Animation of Fluids p. 1/2 Realistic Animation of Fluids Nick Foster and Dimitri Metaxas Realistic Animation of Fluids p. 2/2 Overview Problem Statement Previous Work Navier-Stokes Equations

### Navier-Stokes & Flow Simulation

Last Time? Navier-Stokes & Flow Simulation Implicit Surfaces Marching Cubes/Tetras Collision Detection & Response Conservative Bounding Regions backtracking fixing Today Flow Simulations in Graphics Flow

### Acknowledgements. Prof. Dan Negrut Prof. Darryl Thelen Prof. Michael Zinn. SBEL Colleagues: Hammad Mazar, Toby Heyn, Manoj Kumar

Philipp Hahn Acknowledgements Prof. Dan Negrut Prof. Darryl Thelen Prof. Michael Zinn SBEL Colleagues: Hammad Mazar, Toby Heyn, Manoj Kumar 2 Outline Motivation Lumped Mass Model Model properties Simulation

### Divergence-Free Smoothed Particle Hydrodynamics

Copyright of figures and other materials in the paper belongs to original authors. Divergence-Free Smoothed Particle Hydrodynamics Bender et al. SCA 2015 Presented by MyungJin Choi 2016-11-26 1. Introduction

### Dynamical Simulation 1: Particle Systems and ODEs

CS-C3100 Computer Graphics Fall 2017 Jaakko Lehtinen Markus Kettunen Dynamical Simulation 1: Particle Systems and ODEs 1 Futuremark Corp., used with permission Types of Animation Keyframing Procedural

### NVIDIA. Interacting with Particle Simulation in Maya using CUDA & Maximus. Wil Braithwaite NVIDIA Applied Engineering Digital Film

NVIDIA Interacting with Particle Simulation in Maya using CUDA & Maximus Wil Braithwaite NVIDIA Applied Engineering Digital Film Some particle milestones FX Rendering Physics 1982 - First CG particle FX

### Overview of Traditional Surface Tracking Methods

Liquid Simulation With Mesh-Based Surface Tracking Overview of Traditional Surface Tracking Methods Matthias Müller Introduction Research lead of NVIDIA PhysX team PhysX GPU acc. Game physics engine www.nvidia.com\physx

### PHYSICALLY BASED ANIMATION

PHYSICALLY BASED ANIMATION CS148 Introduction to Computer Graphics and Imaging David Hyde August 2 nd, 2016 WHAT IS PHYSICS? the study of everything? WHAT IS COMPUTATION? the study of everything? OUTLINE

### 2.11 Particle Systems

2.11 Particle Systems 320491: Advanced Graphics - Chapter 2 152 Particle Systems Lagrangian method not mesh-based set of particles to model time-dependent phenomena such as snow fire smoke 320491: Advanced

### IMPROVED WALL BOUNDARY CONDITIONS WITH IMPLICITLY DEFINED WALLS FOR PARTICLE BASED FLUID SIMULATION

6th European Conference on Computational Mechanics (ECCM 6) 7th European Conference on Computational Fluid Dynamics (ECFD 7) 1115 June 2018, Glasgow, UK IMPROVED WALL BOUNDARY CONDITIONS WITH IMPLICITLY

### Shape of Things to Come: Next-Gen Physics Deep Dive

Shape of Things to Come: Next-Gen Physics Deep Dive Jean Pierre Bordes NVIDIA Corporation Free PhysX on CUDA PhysX by NVIDIA since March 2008 PhysX on CUDA available: August 2008 GPU PhysX in Games Physical

### Thermal Coupling Method Between SPH Particles and Solid Elements in LS-DYNA

Thermal Coupling Method Between SPH Particles and Solid Elements in LS-DYNA Jingxiao Xu 1, Jason Wang 2 1 LSTC 2 LSTC 1 Abstract Smooth particles hydrodynamics is a meshfree, Lagrangian particle method

### Example 13 - Shock Tube

Example 13 - Shock Tube Summary This famous experiment is interesting for observing the shock-wave propagation. Moreover, this case uses the representation of perfect gas and compares the different formulations:

### Comparison between incompressible SPH solvers

2017 21st International Conference on Control Systems and Computer Science Comparison between incompressible SPH solvers Claudiu Baronea, Adrian Cojocaru, Mihai Francu, Anca Morar, Victor Asavei Computer

### Interactive Fluid Simulation using Augmented Reality Interface

Interactive Fluid Simulation using Augmented Reality Interface Makoto Fuisawa 1, Hirokazu Kato 1 1 Graduate School of Information Science, Nara Institute of Science and Technology, 8916-5 Takayama, Ikoma,

### Finite Volume Discretization on Irregular Voronoi Grids

Finite Volume Discretization on Irregular Voronoi Grids C.Huettig 1, W. Moore 1 1 Hampton University / National Institute of Aerospace Folie 1 The earth and its terrestrial neighbors NASA Colin Rose, Dorling

### Smoke Simulation using Smoothed Particle Hydrodynamics (SPH) Shruti Jain MSc Computer Animation and Visual Eects Bournemouth University

Smoke Simulation using Smoothed Particle Hydrodynamics (SPH) Shruti Jain MSc Computer Animation and Visual Eects Bournemouth University 21st November 2014 1 Abstract This report is based on the implementation

### The 3D DSC in Fluid Simulation

The 3D DSC in Fluid Simulation Marek K. Misztal Informatics and Mathematical Modelling, Technical University of Denmark mkm@imm.dtu.dk DSC 2011 Workshop Kgs. Lyngby, 26th August 2011 Governing Equations

### Hardware Accelerated Real-Time Fluid Surface Simulation

Hardware Accelerated Real-Time Fluid Surface Simulation Björn Hellstrandh bjornh@cs.umu.se Jesper Byström c99jbm@cs.umu.se July 1, 2008 Master s Thesis in Computing Science, 2*30 ECTS credits Supervisor

### Support for Multi physics in Chrono

Support for Multi physics in Chrono The Story Ahead Overview of multi physics strategy in Chrono Summary of handling rigid/flexible body dynamics using Lagrangian approach Summary of handling fluid, and

### Adarsh Krishnamurthy (cs184-bb) Bela Stepanova (cs184-bs)

OBJECTIVE FLUID SIMULATIONS Adarsh Krishnamurthy (cs184-bb) Bela Stepanova (cs184-bs) The basic objective of the project is the implementation of the paper Stable Fluids (Jos Stam, SIGGRAPH 99). The final

### Modeling of Granular Materials

Modeling of Granular Materials Abhinav Golas COMP 768 - Physically Based Simulation April 23, 2009 1 Motivation Movies, games Spiderman 3 Engineering design grain silos Avalanches, Landslides The Mummy

### Solidification using Smoothed Particle Hydrodynamics

Solidification using Smoothed Particle Hydrodynamics Master Thesis CA-3817512 Game and Media Technology Utrecht University, The Netherlands Supervisors: dr. ir. J.Egges dr. N.G. Pronost July, 2014 - 2

### Constraint fluids in Sprinkle. Dennis Gustafsson Mediocre

Constraint fluids in Sprinkle Dennis Gustafsson Mediocre Sprinkle. Sequel. Put out fires. Makeshift firetruck. Distant moon of Saturn. Fluid sim used at the core. Not only to put out fires -> move obstacles,

### T6: Position-Based Simulation Methods in Computer Graphics. Jan Bender Miles Macklin Matthias Müller

T6: Position-Based Simulation Methods in Computer Graphics Jan Bender Miles Macklin Matthias Müller Jan Bender Organizer Professor at the Visual Computing Institute at Aachen University Research topics

### 3D Simulation of Dam-break effect on a Solid Wall using Smoothed Particle Hydrodynamic

ISCS 2013 Selected Papers Dam-break effect on a Solid Wall 1 3D Simulation of Dam-break effect on a Solid Wall using Smoothed Particle Hydrodynamic Suprijadi a,b, F. Faizal b, C.F. Naa a and A.Trisnawan

### Mass-Spring Systems. Last Time?

Mass-Spring Systems Last Time? Implicit Surfaces & Marching Cubes/Tetras Collision Detection & Conservative Bounding Regions Spatial Acceleration Data Structures Octree, k-d tree, BSF tree 1 Today Particle

### PARALLEL SIMULATION OF A FLUID FLOW BY MEANS OF THE SPH METHOD: OPENMP VS. MPI COMPARISON. Pawe l Wróblewski, Krzysztof Boryczko

Computing and Informatics, Vol. 28, 2009, 139 150 PARALLEL SIMULATION OF A FLUID FLOW BY MEANS OF THE SPH METHOD: OPENMP VS. MPI COMPARISON Pawe l Wróblewski, Krzysztof Boryczko Department of Computer

### Simulation in Computer Graphics. Introduction. Matthias Teschner. Computer Science Department University of Freiburg

Simulation in Computer Graphics Introduction Matthias Teschner Computer Science Department University of Freiburg Contact Matthias Teschner Computer Graphics University of Freiburg Georges-Koehler-Allee

### Simulation of liquid cube fracture with SPH

Journal of Physics: Conference Series PAPER OPEN ACCESS Simulation of liquid cube fracture with SPH To cite this article: M N Davydov 2016 J. Phys.: Conf. Ser. 754 062001 View the article online for updates

### CUDA. Fluid simulation Lattice Boltzmann Models Cellular Automata

CUDA Fluid simulation Lattice Boltzmann Models Cellular Automata Please excuse my layout of slides for the remaining part of the talk! Fluid Simulation Navier Stokes equations for incompressible fluids

### Animation of Fluids. Animating Fluid is Hard

Animation of Fluids Animating Fluid is Hard Too complex to animate by hand Surface is changing very quickly Lots of small details In short, a nightmare! Need automatic simulations AdHoc Methods Some simple

### Technical Report TR

Technical Report TR-2015-09 Boundary condition enforcing methods for smoothed particle hydrodynamics Arman Pazouki 1, Baofang Song 2, Dan Negrut 1 1 University of Wisconsin-Madison, Madison, WI, 53706-1572,

### Interactive Fluid Simulation Using Augmented Reality Interface

Interactive Fluid Simulation Using Augmented Reality Interface Makoto Fuisawa and Hirokazu Kato Graduate School of Information Science, Nara Institute of Science and Technology, 8916-5 Takayama, Ikoma,

### Thermal Coupling Method Between SPH Particles and Solid Elements in LS-DYNA

Thermal Coupling Method Between SPH Particles and Solid Elements in LS-DYNA INTRODUCTION: Jingxiao Xu, Jason Wang LSTC Heat transfer is very important in many industrial and geophysical problems. Many

### ALE Seamless Immersed Boundary Method with Overset Grid System for Multiple Moving Objects

Tenth International Conference on Computational Fluid Dynamics (ICCFD10), Barcelona,Spain, July 9-13, 2018 ICCFD10-047 ALE Seamless Immersed Boundary Method with Overset Grid System for Multiple Moving

### CS205b/CME306. Lecture 9

CS205b/CME306 Lecture 9 1 Convection Supplementary Reading: Osher and Fedkiw, Sections 3.3 and 3.5; Leveque, Sections 6.7, 8.3, 10.2, 10.4. For a reference on Newton polynomial interpolation via divided

### Topics in Computer Animation

Topics in Computer Animation Animation Techniques Artist Driven animation The artist draws some frames (keyframing) Usually in 2D The computer generates intermediate frames using interpolation The old

### Index FEATURES LIST 2

FULL FEATURES LIST Index RealFlow Features 4 Liquids 4 Elastics 4 Granulars 4 Rigids 5 Viscous Materials 5 Viscoelastic Materials 5 Fibres 5 Built-in Basic Primitives 6 Particle Emitters 6 Rigid Bodies

### Continued Investigation of Small-Scale Air-Sea Coupled Dynamics Using CBLAST Data

Continued Investigation of Small-Scale Air-Sea Coupled Dynamics Using CBLAST Data Dick K.P. Yue Center for Ocean Engineering Department of Mechanical Engineering Massachusetts Institute of Technology Cambridge,

### FEMLAB Exercise 1 for ChE366

FEMLAB Exercise 1 for ChE366 Problem statement Consider a spherical particle of radius r s moving with constant velocity U in an infinitely long cylinder of radius R that contains a Newtonian fluid. Let

### Chapter 1 - Basic Equations

2.20 Marine Hydrodynamics, Fall 2017 Lecture 2 Copyright c 2017 MIT - Department of Mechanical Engineering, All rights reserved. 2.20 Marine Hydrodynamics Lecture 2 Chapter 1 - Basic Equations 1.1 Description

### Level set methods Formulation of Interface Propagation Boundary Value PDE Initial Value PDE Motion in an externally generated velocity field

Level Set Methods Overview Level set methods Formulation of Interface Propagation Boundary Value PDE Initial Value PDE Motion in an externally generated velocity field Convection Upwind ddifferencingi

### Parallel GPU-Based Fluid Animation. Master s thesis in Interaction Design and Technologies JAKOB SVENSSON

Parallel GPU-Based Fluid Animation Master s thesis in Interaction Design and Technologies JAKOB SVENSSON Department of Applied Information Technology CHALMERS UNIVERSITY OF TECHNOLOGY Gothenburg, Sweden

### Coupling of STAR-CCM+ to Other Theoretical or Numerical Solutions. Milovan Perić

Coupling of STAR-CCM+ to Other Theoretical or Numerical Solutions Milovan Perić Contents The need to couple STAR-CCM+ with other theoretical or numerical solutions Coupling approaches: surface and volume

### Isogeometric Analysis of Fluid-Structure Interaction

Isogeometric Analysis of Fluid-Structure Interaction Y. Bazilevs, V.M. Calo, T.J.R. Hughes Institute for Computational Engineering and Sciences, The University of Texas at Austin, USA e-mail: {bazily,victor,hughes}@ices.utexas.edu

### Chapter 19- Object Physics

Chapter 19- Object Physics Flowing water, fabric, things falling, and even a bouncing ball can be difficult to animate realistically using techniques we have already discussed. This is where Blender's

### Investigating The Stability of The Balance-force Continuum Surface Force Model of Surface Tension In Interfacial Flow

Investigating The Stability of The Balance-force Continuum Surface Force Model of Surface Tension In Interfacial Flow Vinh The Nguyen University of Massachusetts Dartmouth Computational Science Training

### Ship in a Bottle. 1 Modeling and Rendering the Water. Saket Patkar and Bo Zhu

Ship in a Bottle Saket Patkar and Bo Zhu 1 Modeling and Rendering the Water We decided to get the basic ocean surface through a particle level set fluid simulation. The fluid simulator can only handle

### More Animation Techniques

CS 231 More Animation Techniques So much more Animation Procedural animation Particle systems Free-form deformation Natural Phenomena 1 Procedural Animation Rule based animation that changes/evolves over

### Flow Structures Extracted from Visualization Images: Vector Fields and Topology

Flow Structures Extracted from Visualization Images: Vector Fields and Topology Tianshu Liu Department of Mechanical & Aerospace Engineering Western Michigan University, Kalamazoo, MI 49008, USA We live

### A Geometric Approach to Animating Thin Surface Features in SPH Water

A Geometric Approach to Animating Thin Surface Features in SPH Water Taekwon Jang et al. Computer Animation and Social Agents 2013 (CASA) Jong-Hyun Kim 2013. 11.08 Abstract We propose a geometric approach

### Simulation of Fuel Sloshing Comparative Study

3. LS-DYNA Anwenderforum, Bamberg 2004 Netfreie Verfahren Simulation of Fuel Sloshing Comparative Study Matej Vesenjak 1, Heiner Müllerschön 2, Alexander Hummel 3, Zoran Ren 1 1 University of Maribor,

### Chapter 3: Computer Animation Reminder: Descriptive animation. Procedural animation : Examples. Towards methods that generate motion?

Chapter 3 : Computer Animation (continued) Chapter 3: Computer Animation Reminder: Descriptive animation Describes a single motion, with manual control Ex: direct kinematics with key-frames, inverse kinematics

### Inverse Kinematics (part 1) CSE169: Computer Animation Instructor: Steve Rotenberg UCSD, Winter 2018

Inverse Kinematics (part 1) CSE169: Computer Animation Instructor: Steve Rotenberg UCSD, Winter 2018 Welman, 1993 Inverse Kinematics and Geometric Constraints for Articulated Figure Manipulation, Chris

### CNM 190, pt 2 Advanced Digital Animation Lec 03 : Art Direction on Madagascar / Effects 1

Jungle shot from Madagascar CNM 190, pt 2 Advanced Digital Animation Lec 03 : Art Direction on Madagascar / Effects 1 Shannon Jeffries, PDI/Dreamworks (Art Director, Madagascar) Marilyn Friedman, PDI/Dreamworks

### Collision Detection based on Spatial Partitioning

Simulation in Computer Graphics Collision Detection based on Spatial Partitioning Matthias Teschner Computer Science Department University of Freiburg Outline introduction uniform grid Octree and k-d tree

### Solution for Euler Equations Lagrangian and Eulerian Descriptions

Solution for Euler Equations Lagrangian and Eulerian Descriptions Valdir Monteiro dos Santos Godoi valdir.msgodoi@gmail.com Abstract We find an exact solution for the system of Euler equations, supposing

### CFD MODELING FOR PNEUMATIC CONVEYING

CFD MODELING FOR PNEUMATIC CONVEYING Arvind Kumar 1, D.R. Kaushal 2, Navneet Kumar 3 1 Associate Professor YMCAUST, Faridabad 2 Associate Professor, IIT, Delhi 3 Research Scholar IIT, Delhi e-mail: arvindeem@yahoo.co.in

### Simulation of Swirling Bubbly Water using Bubble Particles

Noname manuscript No. (will be inserted by the editor) Simulation of Swirling Bubbly Water using Bubble Particles Ho-Young Lee Jeong-Mo Hong Chang-Hun Kim Received: date / Accepted: date Abstract The effect

### Transfer and pouring processes of casting by smoothed particle. hydrodynamic method

Transfer and pouring processes of casting by smoothed particle hydrodynamic method M. Kazama¹, K. Ogasawara¹, *T. Suwa¹, H. Ito 2, and Y. Maeda 2 1 Application development div., Next generation technical

### Simulation in Computer Graphics Space Subdivision. Matthias Teschner

Simulation in Computer Graphics Space Subdivision Matthias Teschner Outline Introduction Uniform grid Octree and k-d tree BSP tree University of Freiburg Computer Science Department 2 Model Partitioning

### Solving Partial Differential Equations on Overlapping Grids

**FULL TITLE** ASP Conference Series, Vol. **VOLUME**, **YEAR OF PUBLICATION** **NAMES OF EDITORS** Solving Partial Differential Equations on Overlapping Grids William D. Henshaw Centre for Applied Scientific

### Surface Tension Approximation in Semi-Lagrangian Level Set Based Fluid Simulations for Computer Graphics

Surface Tension Approximation in Semi-Lagrangian Level Set Based Fluid Simulations for Computer Graphics Israel Pineda and Oubong Gwun Chonbuk National University israel_pineda_arias@yahoo.com, obgwun@jbnu.ac.kr

### AN ADAPTIVE SAMPLING APPROACH TO INCOMPRESSIBLE PARTICLE-BASED FLUID. A Dissertation WOO-SUCK HONG

AN ADAPTIVE SAMPLING APPROACH TO INCOMPRESSIBLE PARTICLE-BASED FLUID A Dissertation by WOO-SUCK HONG Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment of the requirements

### ALE and Fluid-Structure Interaction in LS-DYNA March 2004

ALE and Fluid-Structure Interaction in LS-DYNA March 2004 Workshop Models 1. Taylor bar impact 2. One-dimensional advection test 3. Channel 4. Underwater explosion 5. Bar impacting water surface 6. Sloshing

### Introduction to Computer Graphics. Animation (2) May 26, 2016 Kenshi Takayama

Introduction to Computer Graphics Animation (2) May 26, 2016 Kenshi Takayama Physically-based deformations 2 Simple example: single mass & spring in 1D Mass m, position x, spring coefficient k, rest length

### A Novel Approach to High Speed Collision

A Novel Approach to High Speed Collision Avril Slone University of Greenwich Motivation High Speed Impact Currently a very active research area. Generic projectile- target collision 11 th September 2001.

### (LSS Erlangen, Simon Bogner, Ulrich Rüde, Thomas Pohl, Nils Thürey in collaboration with many more

Parallel Free-Surface Extension of the Lattice-Boltzmann Method A Lattice-Boltzmann Approach for Simulation of Two-Phase Flows Stefan Donath (LSS Erlangen, stefan.donath@informatik.uni-erlangen.de) Simon

### Robust Simulation of Sparsely Sampled Thin Features in SPH-Based Free Surface Flows

Copyright of figures and other materials in the paper belong to original authors. Robust Simulation of Sparsely Sampled Thin Features in SPH-Based Free Surface Flows Xiaowei He et al. ACM SIGGRAPH 2015

### Characteristic Aspects of SPH Solutions

Characteristic Aspects of SPH Solutions for Free Surface Problems: Source and Possible Treatment of High Frequency Numerical Oscillations of Local Loads. A. Colagrossi*, D. Le Touzé & G.Colicchio* *INSEAN

### An Adaptive Sampling Approach to Incompressible Particle-Based Fluid

EG UK Theory and Practice of Computer Graphics (2009) Ik Soo Lim, Wen Tang (Editors) An Adaptive Sampling Approach to Incompressible Particle-Based Fluid Woosuck Hong 1, Donald H. House 2 and John Keyser

### The Jello Cube Assignment 1, CSCI 520. Jernej Barbic, USC

The Jello Cube Assignment 1, CSCI 520 Jernej Barbic, USC 1 The jello cube Undeformed cube Deformed cube The jello cube is elastic, Can be bent, stretched, squeezed,, Without external forces, it eventually

### Adaptive Particles for Incompressible Fluid Simulation (Technical Report tamu-cs-tr )

Adaptive Particles for Incompressible Fluid Simulation (Technical Report tamu-cs-tr 2007-7-2) Woosuck Hong Dept. of Computer Science Texas A&M University wshong@cs.tamu.edu Donald H. House Visualization

### Introduction to geodynamic modelling Introduction to DOUAR

Introduction to geodynamic modelling Introduction to DOUAR David Whipp and Lars Kaislaniemi Department of Geosciences and Geography, Univ. Helsinki 1 Goals of this lecture Introduce DOUAR, a 3D thermomechanical

### Visualization Computer Graphics I Lecture 20

15-462 Computer Graphics I Lecture 20 Visualization Height Fields and Contours Scalar Fields Volume Rendering Vector Fields [Angel Ch. 12] November 20, 2003 Doug James Carnegie Mellon University http://www.cs.cmu.edu/~djames/15-462/fall03

### Vector Visualization. CSC 7443: Scientific Information Visualization

Vector Visualization Vector data A vector is an object with direction and length v = (v x,v y,v z ) A vector field is a field which associates a vector with each point in space The vector data is 3D representation

### Abstract. Introduction. Kevin Todisco

- Kevin Todisco Figure 1: A large scale example of the simulation. The leftmost image shows the beginning of the test case, and shows how the fluid refracts the environment around it. The middle image

### Modelling of Impact on a Fuel Tank Using Smoothed Particle Hydrodynamics

Modelling of Impact on a Fuel Tank Using Smoothed Particle Hydrodynamics R. Vignjevic a, T. De Vuyst a, J. Campbell a, N. Bourne b School of Engineering, Cranfield University, Bedfordshire, MK43 0AL, UK.

Convergent Science White Paper COPYRIGHT 2017 CONVERGENT SCIENCE. All rights reserved. This document contains information that is proprietary to Convergent Science. Public dissemination of this document

### A Particle Cellular Automata Model for Fluid Simulations

Annals of University of Craiova, Math. Comp. Sci. Ser. Volume 36(2), 2009, Pages 35 41 ISSN: 1223-6934 A Particle Cellular Automata Model for Fluid Simulations Costin-Radu Boldea Abstract. A new cellular-automaton

### The Immersed Interface Method

The Immersed Interface Method Numerical Solutions of PDEs Involving Interfaces and Irregular Domains Zhiiin Li Kazufumi Ito North Carolina State University Raleigh, North Carolina Society for Industrial

### An explicit and conservative remapping strategy for semi-lagrangian advection

An explicit and conservative remapping strategy for semi-lagrangian advection Sebastian Reich Universität Potsdam, Potsdam, Germany January 17, 2007 Abstract A conservative semi-lagrangian advection scheme