FLUID SIMULATION. Kristofer Schlachter
|
|
- Caroline Watkins
- 5 years ago
- Views:
Transcription
1 FLUID SIMULATION Kristofer Schlachter
2 The Equations = (r u)u 1 rp + vr2 u + F Incompressibility condition r u =0
3 Breakdown The derivative of velocity with respect to time. Calculated at each grid point each time step. (r u)u The convection term. This is the self advection term. In the code we will use the backward particle trace for this term. r The pressure term. is the density of the fluid vr 2 u or The viscosity term. We are actually going to ignore this term. When you do that you are actually vr ru r r using the Euler Equations. External force. Any external forces including F External force. Any external forces including gravity.
4 Breakdown 1 rp r cle trace for this term. The pressure term. is the density of the fluid a and p is the pressure. p is whatever it takes to make the velocity field divergence free. The simulator will solve for a pressure that makes our fluid incompressible at each time step. a density of water 1000 kg m 2
5 3 Incompressible Euler Equations If you drop the viscosity term from the incompressible Navier Stokes equations +(r u)u + 1 rp = F (4) r u =0 (5) Such an ideal fluid with no viscosity is called inviscid. These are the equations we are going to use.
6 How do we discretize the equations?
7 A Simple Grid We could put all our fluid variables at the nodes of a regular grid But this causes some major problems In 1D: incompressibility means Approximate at a grid point: u x = 0 u i+1 u i 1 2Δx Note the velocity at the grid point isn t involved! = 0 [Bridson 07]
8 A Simple Grid Disaster The only solutions to u x = 0 are u=constant But our numerical version has other solutions: u x [Bridson 07]
9 Staggered Grids Problem is solved if we don t skip over grid points To make it unbiased, we stagger the grid: put velocities halfway between grid points In 1D, we estimate divergence at a grid point as: Problem solved! u x (x i ) u i+ 1 2 u i 1 2 Δx [Bridson 07]
10 The MAC Grid From the Marker-and-Cell (MAC) method [Harlow&Welch 65] A particular staggering of variables in 2D/3D that works well for incompressible fluids: Grid cell (i,j,k) has pressure p i,j,k at its center x-part of velocity u i+1/2,jk in middle of x-face between grid cells (i,j,k) and (i+1,j,k) y-part of velocity v i,j+1/2,k in middle of y-face z-part of velocity w i,j,k+1/2 in middle of z-face [Bridson 07]
11 MAC Grid in 2D p i, j +1 v i, j p i 1, j p i, j p i+1, j u i 1 2, j u i+ 1 2, j v i, j 1 2 p i, j 1 [Bridson 07]
12 Math on a MAC Grid The partial derivative (@). tral y, z) = f(x, y f(x, y, z) ent operator r The gradient operator (r) 0 1 f(x +1,y,z) f(x, y, z), B C rf(x, y, z) f(x, y +1,z) f(x, y, z), A f(x, y, z +1) f(x, y, z)
13 Math on a MAC Grid The divergence of a vector field (r ) r u(x, y, z) =(u x (x +1,y,z) The Laplacian operator (r 2 ) or (r r). gradient operators. u x (x, y, z))+ (u y (x, y +1,z) u y (x, y, z))+ (u z (x, y, z +1) u z (x, y, z)) r 2 f(x, y, z) =f(x +1,y,z)+f(x f(x, y +1,z)+f(x, y 1,y,z)+ 1,z)+ f(x, y, z +1)+f(x, y, z 1) 6f(x, y, z) *There might be a one over h squared term missing
14 Simulation Set u A = advect(u n, t, u n ) Add u B = u A + tf Set u n+1 = project( t, u B ) *I am ignoring choosing a time step in this presentation
15 Advection Figure 3: Basic idea behind the advection step. Instead of moving the cell centers forward in time (b) through the velocity field shown in (a), we look for the particles which end up exactly at the cell centers by tracing backwards in time from the cell centers (c). [Stam 2003]
16 onfused by the e[david Cline ] Advection x mid = x G 1 2 tu (x G) x p = x G tu (x mid ) q n+1 G = interpolate (q n,x p ) he new value of the quantity(velocit
17 Projection The project( t, u) routine does the following: Calculate the negative divergence b (the right-hand side) Set the entries of A If using CG - Construct the MIC(0) preconditioner. Solve Ap = b with a linear solver. If using CG then solve with MICCG(0), i.e., the PCG algorithm with MIC(0) as preconditioner. Compute the new velocities n n+1 according to the pressuregradient update to u.
18 Projection Setting up the divergence vector b (the right hand side) r u(x, y, z) =(u x (x +1,y,z) u x (x, y, z))+ (u y (x, y +1,z) u y (x, y, z))+ (u z (x, y, z +1) u z (x, y, z))
19 Projection 7 Setting up the matrix 2 1 1, ,n 2. 2, n 1,n 1 n,1 n,n 1 n p 1 p 2.. p n = D 1 D 2. D n Where Di corresponds to the divergences through cell i. Ωi is the number of nonsolid neighbors of cell i, and βi,j takes values based upon the equation: i,j = ( 1 if cell i is a neighbor of cell j 0 otherwise This matrix is well known. It is called a 7 Point Laplacian Matrix
20 Projection Calculate the pressure gradient and subtract it from the velocity field to ensure it is divergence free: u n+1 i+ 1 2,j,k = un i+ 1 2,j,k t 1 p i+1,j,k x p i,j,k v n+1 i,j+ 1 2,k = vn i,j+ 1 2,k t 1 p i,j+1,k x p i,j,k w n+1 i,j,k+ 1 2 = w n i,j,k+ 1 2 t 1 p i,j,k+ x p i,j,k
21 Demo
22 Implementation Mapping to Mechanisms: Stencils Common example ( 5-point stencil ): u n+1 i,j = 1 h 2 ( 4un i,j+u n i 1,j+u n i+1,j + u n i,j 1 + u n i,j+1) Sequential OpenMP? MPI? GPU 2D? GPU 3D? Remember this slide from the last lecture? Visualization Parallel Patterns
23 Implementation Thoughts on optimization for parallel execution The most time consuming part of the sim is the pressure solve so the optimization should start with solving it quickly. Optimizations for serial & CPU: Blocking: Cache coherent. Can send blocks to different cores Optimizations for GPU: Do blocking again using local memory to store each block. For 3D use slicing, 3 Slices at a time putting middle slice (block) in local memory.
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
More informationCS 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)
More informationCUDA. 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
More informationCGT 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
More informationNavier-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
More informationOverview 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
More informationNavier-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
More informationRealistic 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
More informationFluid 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
More informationAdarsh 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
More informationRealistic 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
More informationNavier-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
More informationPHYSICALLY 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
More informationRealtime 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
More information2.7 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
More informationCMPT 898 Final Report. Adam L. Preuss. Numerical Simulation Laboratory. Department of Computer Science. University of Saskatchewan
A GPU implementation of massively parallel direction splitting for the incompressible Navier Stokes equations CMPT 898 Final Report Adam L. Preuss Numerical Simulation Laboratory Department of Computer
More informationDivergence-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
More informationAnimation 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
More informationThe 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
More informationWater. 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
More informationFinite 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
More informationA High Quality, Eulerian 3D Fluid Solver in C++ A Senior Project. presented to. the Faculty of the Computer Science Department of
A High Quality, Eulerian 3D Fluid Solver in C++ A Senior Project presented to the Faculty of the Computer Science Department of California Polytechnic State University, San Luis Obispo In Partial Fulfillment
More informationCS GPU and GPGPU Programming Lecture 2: Introduction; GPU Architecture 1. Markus Hadwiger, KAUST
CS 380 - GPU and GPGPU Programming Lecture 2: Introduction; GPU Architecture 1 Markus Hadwiger, KAUST Reading Assignment #2 (until Feb. 17) Read (required): GLSL book, chapter 4 (The OpenGL Programmable
More informationComputer animation for fluid simulation of a high viscous fluid melting
2 nd WIETE Annual Conference on Engineering and Technology Education 2011 WIETE Pattaya, Thailand, 25-28 January 2011 Computer animation for fluid simulation of a high viscous fluid melting S. Lertkulvanich
More informationRealistic Smoke Simulation Using A Frustum Aligned Grid
Realistic Smoke Simulation Using A Frustum Aligned Grid by Alan Wai Lun Woo B.Sc., University of British Columbia, 00 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER
More informationcuibm A GPU Accelerated Immersed Boundary Method
cuibm A GPU Accelerated Immersed Boundary Method S. K. Layton, A. Krishnan and L. A. Barba Corresponding author: labarba@bu.edu Department of Mechanical Engineering, Boston University, Boston, MA, 225,
More informationAbout Phoenix FD PLUGIN FOR 3DS MAX AND MAYA. SIMULATING AND RENDERING BOTH LIQUIDS AND FIRE/SMOKE. USED IN MOVIES, GAMES AND COMMERCIALS.
About Phoenix FD PLUGIN FOR 3DS MAX AND MAYA. SIMULATING AND RENDERING BOTH LIQUIDS AND FIRE/SMOKE. USED IN MOVIES, GAMES AND COMMERCIALS. Phoenix FD core SIMULATION & RENDERING. SIMULATION CORE - GRID-BASED
More informationSurface 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
More informationSimple and Fast Fluids
Simple and Fast Fluids Martin Guay, Fabrice Colin, Richard Egli To cite this version: Martin Guay, Fabrice Colin, Richard Egli. Simple and Fast Fluids. GPU Pro, A.K. Peters, Ltd., 2011, GPU Pro, pp.433-444.
More informationSmoke 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
More informationTwo-Phase flows on massively parallel multi-gpu clusters
Two-Phase flows on massively parallel multi-gpu clusters Peter Zaspel Michael Griebel Institute for Numerical Simulation Rheinische Friedrich-Wilhelms-Universität Bonn Workshop Programming of Heterogeneous
More informationThe 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
More informationAvailable online at ScienceDirect. Parallel Computational Fluid Dynamics Conference (ParCFD2013)
Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 61 ( 2013 ) 81 86 Parallel Computational Fluid Dynamics Conference (ParCFD2013) An OpenCL-based parallel CFD code for simulations
More informationLevel 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
More informationAn adaptive discretization of incompressible flow using a multitude of moving Cartesian grids
An adaptive discretization of incompressible flow using a multitude of moving Cartesian grids R. Elliot English, Linhai Qiu, Yue Yu, Ronald Fedkiw Stanford University, 353 Serra Mall Room 27, Stanford,
More informationReal-Time Volumetric Smoke using D3D10. Sarah Tariq and Ignacio Llamas NVIDIA Developer Technology
Real-Time Volumetric Smoke using D3D10 Sarah Tariq and Ignacio Llamas NVIDIA Developer Technology Smoke in NVIDIA s DirectX10 SDK Sample Smoke in the game Hellgate London Talk outline: Why 3D fluid simulation
More informationAN 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
More informationParticle-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,
More informationHYPERDRIVE IMPLEMENTATION AND ANALYSIS OF A PARALLEL, CONJUGATE GRADIENT LINEAR SOLVER PROF. BRYANT PROF. KAYVON 15618: PARALLEL COMPUTER ARCHITECTURE
HYPERDRIVE IMPLEMENTATION AND ANALYSIS OF A PARALLEL, CONJUGATE GRADIENT LINEAR SOLVER AVISHA DHISLE PRERIT RODNEY ADHISLE PRODNEY 15618: PARALLEL COMPUTER ARCHITECTURE PROF. BRYANT PROF. KAYVON LET S
More informationCUDA/OpenGL Fluid Simulation. Nolan Goodnight
CUDA/OpenGL Fluid Simulation Nolan Goodnight ngoodnight@nvidia.com Document Change History Version Date Responsible Reason for Change 0.1 2/22/07 Nolan Goodnight Initial draft 1.0 4/02/07 Nolan Goodnight
More information6.1 Rendering Wet Sand
6. Rendering Wet Sand 6.. Goals The primary goal of this project was to implement a method for rendering sand as a wet porous medium with water flowing into it from within PBRT. The final result was a
More informationFluids 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
More informationFluid Simulation Quality with Violated CFL Condition
Fluid Simulation Quality with Violated CFL Condition Philipp Erler Supervised by: Christian Hafner, Michael Wimmer Institute of Computer Graphics and Algorithms TU Wien Vienna / Austria Abstract Fluid
More informationChapter 6. Semi-Lagrangian Methods
Chapter 6. Semi-Lagrangian Methods References: Durran Chapter 6. Review article by Staniford and Cote (1991) MWR, 119, 2206-2223. 6.1. Introduction Semi-Lagrangian (S-L for short) methods, also called
More informationMultigrid Solvers in CFD. David Emerson. Scientific Computing Department STFC Daresbury Laboratory Daresbury, Warrington, WA4 4AD, UK
Multigrid Solvers in CFD David Emerson Scientific Computing Department STFC Daresbury Laboratory Daresbury, Warrington, WA4 4AD, UK david.emerson@stfc.ac.uk 1 Outline Multigrid: general comments Incompressible
More informationIMPROVED 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
More informationVolcanic Smoke Animation using CML
Volcanic Smoke Animation using CML Ryoichi Mizuno Yoshinori Dobashi Tomoyuki Nishita The University of Tokyo Tokyo, Japan Hokkaido University Sapporo, Hokkaido, Japan {mizuno,nis}@nis-lab.is.s.u-tokyo.ac.jp
More informationEfficient Tridiagonal Solvers for ADI methods and Fluid Simulation
Efficient Tridiagonal Solvers for ADI methods and Fluid Simulation Nikolai Sakharnykh - NVIDIA San Jose Convention Center, San Jose, CA September 21, 2010 Introduction Tridiagonal solvers very popular
More informationMoving Interface Problems: Methods & Applications Tutorial Lecture II
Moving Interface Problems: Methods & Applications Tutorial Lecture II Grétar Tryggvason Worcester Polytechnic Institute Moving Interface Problems and Applications in Fluid Dynamics Singapore National University,
More informationA higher-order finite volume method with collocated grid arrangement for incompressible flows
Computational Methods and Experimental Measurements XVII 109 A higher-order finite volume method with collocated grid arrangement for incompressible flows L. Ramirez 1, X. Nogueira 1, S. Khelladi 2, J.
More informationSolving 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
More information3D ADI Method for Fluid Simulation on Multiple GPUs. Nikolai Sakharnykh, NVIDIA Nikolay Markovskiy, NVIDIA
3D ADI Method for Fluid Simulation on Multiple GPUs Nikolai Sakharnykh, NVIDIA Nikolay Markovskiy, NVIDIA Introduction Fluid simulation using direct numerical methods Gives the most accurate result Requires
More informationFluid Simulation. Dhruv Kore, Giancarlo Gonzalez, and Jenny Sum CS 488: Introduction to Computer Graphics Professor Angus Forbes
Fluid Simulation Dhruv Kore, Giancarlo Gonzalez, and Jenny Sum CS 488: Introduction to Computer Graphics Professor Angus Forbes 1) Introduction Figure 1.1: Realistic water and ice simulation using Blender,
More informationA New Incompressibility Discretization for a Hybrid Particle MAC Grid Representation with Surface Tension
A New Incompressibility Discretization for a Hybrid Particle MAC Grid Representation with Surface Tension Wen Zheng, Bo Zhu, Byungmoon Kim, Ronald Fedkiw Stanford University, 353 Serra Mall Room 207, Stanford,
More informationDrop Impact Simulation with a Velocity-Dependent Contact Angle
ILASS Americas 19th Annual Conference on Liquid Atomization and Spray Systems, Toronto, Canada, May 2006 Drop Impact Simulation with a Velocity-Dependent Contact Angle S. Afkhami and M. Bussmann Department
More informationCONFORMAL MAPPING POTENTIAL FLOW AROUND A WINGSECTION USED AS A TEST CASE FOR THE INVISCID PART OF RANS SOLVERS
European Conference on Computational Fluid Dynamics ECCOMAS CFD 2006 P. Wesseling, E. Oñate and J. Périaux (Eds) c TU Delft, The Netherlands, 2006 CONFORMAL MAPPING POTENTIAL FLOW AROUND A WINGSECTION
More informationParticle-Based Fluid Simulation. CSE169: Computer Animation Steve Rotenberg UCSD, Spring 2016
Particle-Based Fluid Simulation CSE169: Computer Animation Steve Rotenberg UCSD, Spring 2016 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
More informationENERGY-224 Reservoir Simulation Project Report. Ala Alzayer
ENERGY-224 Reservoir Simulation Project Report Ala Alzayer Autumn Quarter December 3, 2014 Contents 1 Objective 2 2 Governing Equations 2 3 Methodolgy 3 3.1 BlockMesh.........................................
More informationA multi-gpu accelerated solver for the three-dimensional two-phase incompressible Navier-Stokes equations
Computer Science - Research and Development manuscript No. (will be inserted by the editor) A multi-gpu accelerated solver for the three-dimensional two-phase incompressible Navier-Stokes equations Michael
More informationOverview. Applications of DEC: Fluid Mechanics and Meshing. Fluid Models (I) Part I. Computational Fluids with DEC. Fluid Models (II) Fluid Models (I)
Applications of DEC: Fluid Mechanics and Meshing Mathieu Desbrun Applied Geometry Lab Overview Putting DEC to good use Fluids, fluids, fluids geometric interpretation of classical models discrete geometric
More informationDriven Cavity Example
BMAppendixI.qxd 11/14/12 6:55 PM Page I-1 I CFD Driven Cavity Example I.1 Problem One of the classic benchmarks in CFD is the driven cavity problem. Consider steady, incompressible, viscous flow in a square
More informationComputational Fluid Dynamics - Incompressible Flows
Computational Fluid Dynamics - Incompressible Flows March 25, 2008 Incompressible Flows Basis Functions Discrete Equations CFD - Incompressible Flows CFD is a Huge field Numerical Techniques for solving
More informationThe Development of a Navier-Stokes Flow Solver with Preconditioning Method on Unstructured Grids
Proceedings of the International MultiConference of Engineers and Computer Scientists 213 Vol II, IMECS 213, March 13-15, 213, Hong Kong The Development of a Navier-Stokes Flow Solver with Preconditioning
More informationCS205b/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
More informationBubble Dynamics using Free Surfaces in a VOF framework
Bubble Dynamics using Free Surfaces in a VOF framework Sevilla Meeting: Numerical Challenges in two-phase flows 27 October 2014 Léon MALAN Supervisor: Prof. Stéphane ZALESKI 1 Contents Introduction: Simulation
More informationShape 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
More informationCNM 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
More information2.29 Numerical Marine Hydrodynamics Spring 2007
Numerical Marine Hydrodynamics Spring 2007 Course Staff: Instructor: Prof. Henrik Schmidt OCW Web Site: http://ocw.mit.edu/ocwweb/mechanical- Engineering/2-29Spring-2003/CourseHome/index.htm Units: (3-0-9)
More informationAn adaptive discretization of incompressible flow using a multitude of moving Cartesian grids
An adaptive discretization of incompressible flow using a multitude of moving Cartesian grids R. Elliot English, Linhai Qiu,YueYu, Ronald Fedkiw Stanford University, 353 Serra Mall Room 27, Stanford, CA
More informationEulerian Smoke Simulation. Brett Lambright (i ) MSc Computer Animation and Visual Effects Bournemouth University - NCCA
Eulerian Smoke Simulation Brett Lambright (i7263347) MSc Computer Animation and Visual Effects Bournemouth University - NCCA 16 August 2013 Contents 1 Introduction 1 2 Previous Work 2 3 Technical Background
More informationEulerian Fluid Simulator
Eulerian Fluid Simulator Liviu-George Bitiușcă MSc Computer Animation & Visual Effects Bournemouth University August 2016 Contents Table of contents... i Abstract...ii 1 Introduction.1 1.1 Motivation 1
More informationAnimating smoke with dynamic balance
COMPUTER ANIMATION AND VIRTUAL WORLDS Comp. Anim. Virtual Worlds 2005; 16: 405 414 Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/cav.87 Natural Phenomena and Special
More informationLagrangian 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
More informationComparison 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
More informationA Performance Optimization Study for the DreamWorks Animation Fluid Solver
A Performance Optimization Study for the DreamWorks Animation Fluid Solver John J. O Neill, Charles Congdon, Ram Ramanujam Intel Corporation Silviu Borac, Ron Henderson DreamWorks Animation July 2010 Abstract
More informationNumerical Methods for PDEs. SSC Workgroup Meetings Juan J. Alonso October 8, SSC Working Group Meetings, JJA 1
Numerical Methods for PDEs SSC Workgroup Meetings Juan J. Alonso October 8, 2001 SSC Working Group Meetings, JJA 1 Overview These notes are meant to be an overview of the various memory access patterns
More informationGPU-based Distributed Behavior Models with CUDA
GPU-based Distributed Behavior Models with CUDA Courtesy: YouTube, ISIS Lab, Universita degli Studi di Salerno Bradly Alicea Introduction Flocking: Reynolds boids algorithm. * models simple local behaviors
More informationAnalysis of the Adjoint Euler Equations as used for Gradient-based Aerodynamic Shape Optimization
Analysis of the Adjoint Euler Equations as used for Gradient-based Aerodynamic Shape Optimization Final Presentation Dylan Jude Graduate Research Assistant University of Maryland AMSC 663/664 May 4, 2017
More informationNVIDIA. 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
More informationFLUENT Secondary flow in a teacup Author: John M. Cimbala, Penn State University Latest revision: 26 January 2016
FLUENT Secondary flow in a teacup Author: John M. Cimbala, Penn State University Latest revision: 26 January 2016 Note: These instructions are based on an older version of FLUENT, and some of the instructions
More informationScalar Field Visualization. Some slices used by Prof. Mike Bailey
Scalar Field Visualization Some slices used by Prof. Mike Bailey Scalar Fields The approximation of certain scalar function in space f(x,y,z). Most of time, they come in as some scalar values defined on
More informationInteraction 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
More informationLattice Boltzmann with CUDA
Lattice Boltzmann with CUDA Lan Shi, Li Yi & Liyuan Zhang Hauptseminar: Multicore Architectures and Programming Page 1 Outline Overview of LBM An usage of LBM Algorithm Implementation in CUDA and Optimization
More informationComputational Fluid Dynamics Simulations using Many Graphics Processors
Computational Fluid Dynamics Simulations using Many Graphics Processors Ali Khajeh-Saeed and J. Blair Perot Theoretical and Computational Fluid Dynamics Laboratory, University of Massachusetts, Amherst,
More informationAnimation and Ray Tracing
CS4620/5620: Lecture 33 Animation and Ray Tracing 2012 Kavita Bala 1 Announcements Quaternion problem, 3.3: 180 degrees 4621 Friday (animation): Nov 16 Plan Ray Tracing Thanksgiving Color Prelim (Thu after
More informationTheodore Kim Michael Henson Ming C.Lim. Jae ho Lim. Korea University Computer Graphics Lab.
Theodore Kim Michael Henson Ming C.Lim Jae ho Lim Abstract Movie Ice formation simulation Present a novel algorithm Motivated by the physical process of ice growth Hybrid algorithm by three techniques
More informationFEMLAB 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
More informationPARALLEL 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
More informationPARALUTION - a Library for Iterative Sparse Methods on CPU and GPU
- a Library for Iterative Sparse Methods on CPU and GPU Dimitar Lukarski Division of Scientific Computing Department of Information Technology Uppsala Programming for Multicore Architectures Research Center
More informationIMMERSED BOUNDARY METHOD FOR SHARED-MEMORY ARCHITECTURES. 1. Introduction
IMMERSED BOUNDARY METHOD FOR SHARED-MEMORY ARCHITECTURES JEFFREY K. WIENS. Abstract. In this report, we propose a novel, massively parallelizable algorithm for the immersed boundary method based on the
More informationRecent applications of overset mesh technology in SC/Tetra
Recent applications of overset mesh technology in SC/Tetra NIA CFD Seminar October 6, 2014 Tomohiro Irie Software Cradle Co., Ltd. 1 Contents Introduction Software Cradle SC/Tetra Background of Demands
More informationHybrid Particle-Grid Water Simulation using Multigrid Pressure Solver
LiU-ITN-TEK-G--14/006-SE Hybrid Particle-Grid Water Simulation using Multigrid Pressure Solver Per Karlsson 2014-03-13 Department of Science and Technology Linköping University SE-601 74 Norrköping, Sweden
More informationAdaptive 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
More informationImagery for 3D geometry design: application to fluid flows.
Imagery for 3D geometry design: application to fluid flows. C. Galusinski, C. Nguyen IMATH, Université du Sud Toulon Var, Supported by ANR Carpeinter May 14, 2010 Toolbox Ginzburg-Landau. Skeleton 3D extension
More informationGPU Methods for Real-Time Haptic Interaction with 3D Fluids
GPU Methods for Real-Time Haptic Interaction with 3D Fluids Meng Yang, Jingwan Lu, Alla Safonova, and Katherine J. Kuchenbecker Microsoft Corporation, Redmond, WA, USA and Information Science, University
More informationLATTICE-BOLTZMANN METHOD FOR THE SIMULATION OF LAMINAR MIXERS
14 th European Conference on Mixing Warszawa, 10-13 September 2012 LATTICE-BOLTZMANN METHOD FOR THE SIMULATION OF LAMINAR MIXERS Felix Muggli a, Laurent Chatagny a, Jonas Lätt b a Sulzer Markets & Technology
More informationAn Efficient Adaptive Vortex Particle Method for Real-Time Smoke Simulation
2011 12th International Conference on Computer-Aided Design and Computer Graphics An Efficient Adaptive Vortex Particle Method for Real-Time Smoke Simulation Shengfeng He 1, *Hon-Cheng Wong 1,2, Un-Hong
More informationContinuum-Microscopic Models
Scientific Computing and Numerical Analysis Seminar October 1, 2010 Outline Heterogeneous Multiscale Method Adaptive Mesh ad Algorithm Refinement Equation-Free Method Incorporates two scales (length, time
More informationLecture 1: Finite Volume WENO Schemes Chi-Wang Shu
Lecture 1: Finite Volume WENO Schemes Chi-Wang Shu Division of Applied Mathematics Brown University Outline of the First Lecture General description of finite volume schemes for conservation laws The WENO
More informationFluid Simulation and Reaction-Diffusion Textures on Surfaces Maria Andrade Luiz Velho (supervisor) Technical Report TR Relatório Técnico
Laboratório VISGRAF Instituto de Matemática Pura e Aplicada Fluid Simulation and Reaction-Diffusion Textures on Surfaces Maria Andrade Luiz Velho (supervisor) Technical Report TR-0-0 Relatório Técnico
More information