Continuum-Microscopic Models
|
|
- Gabriel Mason
- 6 years ago
- Views:
Transcription
1 Scientific Computing and Numerical Analysis Seminar October 1, 2010
2 Outline Heterogeneous Multiscale Method Adaptive Mesh ad Algorithm Refinement Equation-Free Method
3 Incorporates two scales (length, time or both) into one algorithm Different scales = different physical laws General idea behind CM methods: Utilize information from a detailed model to update information for a coarser model CM methods have been applied to a wide variety of applications in biology, chemistry, material science, and fluid mechanics
4 Heterogeneous Multiscale Method Developed by Wienan E and Bjorn Engquist Describe motion of a continuous body (e.g. fluid, gas, elastic material) whose motion is governed by its discrete elements (fluid particles) Modeling all discrete elements is too costly However, to close the continuum level equations, information is needed from the microscopic scale
5 Heterogeneous Multiscale Method Two Numerical Schemes Example: Modeling a particular fluid flow Continuum Level: Navier Stokes with Finite Volume Method Microscopic Level: Molecular Dynamics Equations for fluid particles Figure from and
6 Heterogeneous Multiscale Method Numerical scheme chosen for discretizing and updating the continuum level equations (finite differencing, finite volume) Discretization corresponds to a grid laid over the domain For example, a one-dimensional, finite volume grid looks like this:
7 Heterogeneous Multiscale Method Example 1: Suppose you want to update some macroscopic (continuum-level) quantity U (velocity, density, etc.) U represents the average of u (the equivalent quantity at the microscopic scale) U i would represent the average fluid velocity or fluid density over the grid cell i U i (t) = 1 x x+ x 2 x x 2 u(y, t)dy (1)
8 Heterogeneous Multiscale Method Motion of quantities U or u governed by conservation laws of the form: U t + f (U) x = 0, u t + f (u) x = 0 The quantity changes over time due to any flux of the quantity into or out of an area The flux f (U) is often unknown or difficult to compute for macroscopic models It can be approximated by utilizing a known flux f (u) from the microscopic scale
9 Heterogeneous Multiscale Method Conservation Equation for the macroscopic U variable can be discretized as follows: U(x, t + t) U(x, t) f (u(x + x/2, t) f (u(x x/2, t) + t x where the flux of U is estimated by computing the flux of u exactly, at the boundaries of each grid cell
10 Heterogeneous Multiscale Method Example 2: Constitutive Law Modeling an elastic body motion Constitutive Law of the form: σ = σ(ɛ) is needed Law will contain parameters describing the material s response to mechanical strains For heterogeneous media, these values can vary with location in the material and with time HMM is used to update the mechanical parameters after each time step
11 Heterogeneous Multiscale Method Typical assumption made for this case: the microscopic elements quickly settle to equilibrium The computation of new mechanical parameters can be done with a small number of microscopic time steps The micro-system does not need to be evolved for the full macroscopic size time step
12 Heterogeneous Multiscale Method General Steps of HMM 1 Create a microscopic system based on macroscopic variables, (typically done with normal distributions) 2 Run the microscopic updating scheme 3 Apply an averaging operator to get macroscopic level values from the microscopic results 4 Run the macroscopic updating scheme 5 Repeat Steps 1-4
13 Heterogeneous Multiscale Method Pros and Cons of this Method: Pro: More accurate then just a continuous model Pro: Works well for problems with microscopic processes that settle quickly to equilibrium Con: HMM only works for problems where the micro-structure is well known, or can be reasonably approximated by a known distribution
14 Adaptive Mesh and Algorithm Refinement Developed mainly by Alejandro Garcia AMAR combines the ideas of grid refinement with utilizing different models at different refinement level Example: Navier-Stokes utilized at coarse grid, and a particle method used at the finest grid refinement
15 Adaptive Mesh and Algorithm Refinement Grid Refinement Lay a grid over the domain of the problem As simulation proceeds there may be regions in the domain that contain interesting dynamics Examples: near a boundary, in an area of turbulent flow The grid may need to be refined in these areas to get a better resolution of the solution
16 Adaptive Mesh and Algorithm Refinement Grid Refinement Refinement proceeds until error in grid values is below a certain threshold Can have different depths of refinements in different parts of the domain
17 Adaptive Mesh and Algorithm Refinement Grid Match-up It is important to have variables match-up at the boundaries of different refinement levels Averaging and Interpolation techniques are utilized
18 Adaptive Mesh and Algorithm Refinement If the refinement changes the spatial scale by several orders of magnitude, the equations may also change at this finer scale Example: Coarse grid, Navier Stokes Finest grid, Molecular Dynamics
19 Adaptive Mesh and Algorithm Refinement Basic Algorithm The continuous problem is advanced numerically one continuum-level time step t cont from t i to t i+1 over the whole coarse grid This is done even for coarse grid cells that overlay a finer grid The microscopic problem on the fine grid is also advanced from t i to t i+1 by taking several smaller time steps t micro
20 Adaptive Mesh and Algorithm Refinement Basic Algorithm (continued) The possible interaction of the refined area with its surrounding coarse grid cells is included by a "buffer" region at the boundaries between coarse and fine grids containing microscopic particles. These particles are moved during the microscopic advancement
21 Adaptive Mesh and Algorithm Refinement Basic Algorithm (continued) Any particles in the fine grid or buffer region that cross the boundary are included in the flux computation After all microsteps have been taken, the coarse grid cell overlying the fine grid has its variables updated by averaging the results from the fine scale computation
22 Adaptive Mesh and Algorithm Refinement Example Application: Piston traveling though a gas Shock wave forms as gas compressed Near shock, grid refined to gas particle level Navier-Stokes utilized at the coarse level AMAR captures the shock wave better than purely continuous Navier-Stokes
23 Adaptive Mesh and Algorithm Refinement Pros and Cons to AMAR Pro: Good for problems with small areas requiring refinement Pro: Microscopic problem advanced for full time interval so no microscopic information lost Con: Only useful for problems with small areas of interesting dynamics in the domain
24 Equation-Free Method Developed mainly by Yannis Kevrekidis EFM is similar to HMM in that the goal is to utilize micro-scale information to better model the system at the macro-scale Main difference: macro-scale equations are not explicitly written down and solved (hence the name "Equation-free!")
25 Equation-Free Method Motivation for EFM Sometimes the best description of a problem comes from a microscopic scale Developing a macroscopic scale, constitutive law for this system may be difficult EFM was developed to circumvent this issue Information from the micro-scale is used to estimate macro-scale variables at future points in time
26 Equation-Free Method Simple Example: Let C be some quantity (perhaps a concentration of a chemical) This quantity changes over time according to some law of the form: C = f (C) t Given the current state C n of the quantity, one can estimate C at the next time step with: C n+1 = C n + tf (C n )
27 Equation-Free Method Suppose the function f (C) is unknown However, suppose f (C) at several points in time is known: f (C 0 ), f (C 1 ),...f (C p ) These can be used in a numerical integration scheme to predict C at future points in time
28 Equation-Free Method EFM utilizes short bursts of microscopic computations to evolve microscopic variables c i, f (c i ) These variables are then averaged to compute the f (C i ) type values at the macro-scale The macroscopic f (C i ) s are then used in a numerical integration scheme to predict C at future points in time.
29 Equation-Free Method Algorithm Steps 1 Start with current values for the macroscopic variables 2 Create a microscopic system utilizing distribution functions based on the macroscopic variables 3 Run the computation at the micro-scale for a short number of steps 4 Average the micro-scale variables at each time step to convert them to macroscopic values 5 Estimate future macroscopic variables by utilizing a numerical time integration scheme
30 Equation-Free Method Applications Chemical Reactions Population Dynamics Disease Evolution
31 Equation-Free Method Pros and Cons Pro: Can be utilized for systems where continuum level equations are unknown or difficult to write down or solve Con: The microscopic data is not saved between macroscopic time steps so information can be lost
32 A Look Ahead... The downside to both HMM and EFM is that microscopic data is lost after each continuum time step My Continuum-Microscopic method seeks to correct this issue, by utilizing probability distribution functions to save micro-scale data over time This will be the topic of the next few seminar meetings
33 References E and Engquist, "Multiscale Modeling and Computation", (2003) Notices of the AMS, Vol 50, Number 9, p Garcia et al, "Adaptive Mesh and Algorithm Refinement using Direct Simulation Monte Carlo", (1999) Journal of Computational Physics, Vol 54, Issue 1, p Kevrekidis et al, "Equation-free: The computer-aided analysis of complex multsiscale systems", (2004), AIChE Journal, Vol 50, p
Introduction to Computational Fluid Dynamics Mech 122 D. Fabris, K. Lynch, D. Rich
Introduction to Computational Fluid Dynamics Mech 122 D. Fabris, K. Lynch, D. Rich 1 Computational Fluid dynamics Computational fluid dynamics (CFD) is the analysis of systems involving fluid flow, heat
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY. Analyzing wind flow around the square plate using ADINA Project. Ankur Bajoria
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Analyzing wind flow around the square plate using ADINA 2.094 - Project Ankur Bajoria May 1, 2008 Acknowledgement I would like to thank ADINA R & D, Inc for the full
More informationApplication of Finite Volume Method for Structural Analysis
Application of Finite Volume Method for Structural Analysis Saeed-Reza Sabbagh-Yazdi and Milad Bayatlou Associate Professor, Civil Engineering Department of KNToosi University of Technology, PostGraduate
More informationPreliminary Spray Cooling Simulations Using a Full-Cone Water Spray
39th Dayton-Cincinnati Aerospace Sciences Symposium Preliminary Spray Cooling Simulations Using a Full-Cone Water Spray Murat Dinc Prof. Donald D. Gray (advisor), Prof. John M. Kuhlman, Nicholas L. Hillen,
More information1. Mathematical Modelling
1. describe a given problem with some mathematical formalism in order to get a formal and precise description see fundamental properties due to the abstraction allow a systematic treatment and, thus, solution
More informationAdaptive-Mesh-Refinement Pattern
Adaptive-Mesh-Refinement Pattern I. Problem Data-parallelism is exposed on a geometric mesh structure (either irregular or regular), where each point iteratively communicates with nearby neighboring points
More informationDevelopment of an Integrated Computational Simulation Method for Fluid Driven Structure Movement and Acoustics
Development of an Integrated Computational Simulation Method for Fluid Driven Structure Movement and Acoustics I. Pantle Fachgebiet Strömungsmaschinen Karlsruher Institut für Technologie KIT Motivation
More informationIntroduction to C omputational F luid Dynamics. D. Murrin
Introduction to C omputational F luid Dynamics D. Murrin Computational fluid dynamics (CFD) is the science of predicting fluid flow, heat transfer, mass transfer, chemical reactions, and related phenomena
More informationVerification and Validation in CFD and Heat Transfer: ANSYS Practice and the New ASME Standard
Verification and Validation in CFD and Heat Transfer: ANSYS Practice and the New ASME Standard Dimitri P. Tselepidakis & Lewis Collins ASME 2012 Verification and Validation Symposium May 3 rd, 2012 1 Outline
More informationMultigrid Pattern. I. Problem. II. Driving Forces. III. Solution
Multigrid Pattern I. Problem Problem domain is decomposed into a set of geometric grids, where each element participates in a local computation followed by data exchanges with adjacent neighbors. The grids
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 informationAcknowledgements. 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
More informationCOMPUTER AIDED ENGINEERING. Part-1
COMPUTER AIDED ENGINEERING Course no. 7962 Finite Element Modelling and Simulation Finite Element Modelling and Simulation Part-1 Modeling & Simulation System A system exists and operates in time and space.
More informationModeling Unsteady Compressible Flow
Tutorial 4. Modeling Unsteady Compressible Flow Introduction In this tutorial, FLUENT s density-based implicit solver is used to predict the timedependent flow through a two-dimensional nozzle. As an initial
More informationTurbulent Premixed Combustion with Flamelet Generated Manifolds in COMSOL Multiphysics
Turbulent Premixed Combustion with Flamelet Generated Manifolds in COMSOL Multiphysics Rob J.M Bastiaans* Eindhoven University of Technology *Corresponding author: PO box 512, 5600 MB, Eindhoven, r.j.m.bastiaans@tue.nl
More informationA numerical microscope for plasma physics
A numerical microscope for plasma physics A new simulation capability developed for heavy-ion inertial fusion energy research will accelerate plasma physics and particle beam modeling, with application
More informationHIGH PERFORMANCE COMPUTATION (HPC) FOR THE
HIGH PERFORMANCE COMPUTATION (HPC) FOR THE DEVELOPMENT OF FLUIDIZED BED TECHNOLOGIES FOR BIOMASS GASIFICATION AND CO2 CAPTURE P. Fede, H. Neau, O. Simonin Université de Toulouse; INPT, UPS ; IMFT ; 31400
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 informationPartial Differential Equations
Simulation in Computer Graphics Partial Differential Equations Matthias Teschner Computer Science Department University of Freiburg Motivation various dynamic effects and physical processes are described
More informationFluent User Services Center
Solver Settings 5-1 Using the Solver Setting Solver Parameters Convergence Definition Monitoring Stability Accelerating Convergence Accuracy Grid Independence Adaption Appendix: Background Finite Volume
More informationcomputational Fluid Dynamics - Prof. V. Esfahanian
Three boards categories: Experimental Theoretical Computational Crucial to know all three: Each has their advantages and disadvantages. Require validation and verification. School of Mechanical Engineering
More informationTutorial: Modeling Liquid Reactions in CIJR Using the Eulerian PDF transport (DQMOM-IEM) Model
Tutorial: Modeling Liquid Reactions in CIJR Using the Eulerian PDF transport (DQMOM-IEM) Model Introduction The purpose of this tutorial is to demonstrate setup and solution procedure of liquid chemical
More informationFaculty of Mechanical and Manufacturing Engineering, University Tun Hussein Onn Malaysia (UTHM), Parit Raja, Batu Pahat, Johor, Malaysia
Applied Mechanics and Materials Vol. 393 (2013) pp 305-310 (2013) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/amm.393.305 The Implementation of Cell-Centred Finite Volume Method
More informationHybrid Numerical Methods for Multiscale Simulations of Subsurface Biogeochemical Processes
Hybrid Numerical Methods for Multiscale Simulations of Subsurface Biogeochemical Processes T D Scheibe 1, A M Tartakovsky 1, D M Tartakovsky 2, G D Redden 3 and P Meakin 3 1 Pacific Northwest National
More information14 Dec 94. Hydrocode Micro-Model Concept for Multi-Component Flow in Sediments Hans U. Mair
Hydrocode Micro-Model Concept for Multi-Component Flow in Sediments Hans U. Mair mairh@asme.org Background Hydrocodes are Computational Mechanics tools that simulate the compressible dynamics (i.e., shock
More informationContinued 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,
More informationCHAPTER 1. Introduction
ME 475: Computer-Aided Design of Structures 1-1 CHAPTER 1 Introduction 1.1 Analysis versus Design 1.2 Basic Steps in Analysis 1.3 What is the Finite Element Method? 1.4 Geometrical Representation, Discretization
More informationNonoscillatory Central Schemes on Unstructured Triangular Grids for Hyperbolic Systems of Conservation Laws
Nonoscillatory Central Schemes on Unstructured Triangular Grids for Hyperbolic Systems of Conservation Laws Ivan Christov 1,* Bojan Popov 1 Peter Popov 2 1 Department of Mathematics, 2 Institute for Scientific
More information2D numerical simulation of ocean waves
2D numerical simulation of ocean waves Qingjie. Du,*, Y.C. Dennis. Leung Department of Mechanical Engineering, The University of Hong Kong, Hong Kong, China * Corresponding author. Tel: +852 51743593,
More informationShallow Water Simulations on Graphics Hardware
Shallow Water Simulations on Graphics Hardware Ph.D. Thesis Presentation 2014-06-27 Martin Lilleeng Sætra Outline Introduction Parallel Computing and the GPU Simulating Shallow Water Flow Topics of Thesis
More informationParallel Algorithms: Adaptive Mesh Refinement (AMR) method and its implementation
Parallel Algorithms: Adaptive Mesh Refinement (AMR) method and its implementation Massimiliano Guarrasi m.guarrasi@cineca.it Super Computing Applications and Innovation Department AMR - Introduction Solving
More informationAnalysis, extensions and applications of the Finite-Volume Particle Method (FVPM) PN-II-RU-TE Synthesis of the technical report -
Analysis, extensions and applications of the Finite-Volume Particle Method (FVPM) PN-II-RU-TE-2011-3-0256 - Synthesis of the technical report - Phase 1: Preparation phase Authors: Delia Teleaga, Eliza
More informationExample 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:
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 informationA 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
More informationNUMERICAL VISCOSITY. Convergent Science White Paper. COPYRIGHT 2017 CONVERGENT SCIENCE. All rights reserved.
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
More informationCoping with the Ice Accumulation Problems on Power Transmission Lines
Coping with the Ice Accumulation Problems on Power Transmission Lines P.N. Shivakumar 1, J.F.Peters 2, R.Thulasiram 3, and S.H.Lui 1 1 Department of Mathematics 2 Department of Electrical & Computer Engineering
More informationTeam 194: Aerodynamic Study of Airflow around an Airfoil in the EGI Cloud
Team 194: Aerodynamic Study of Airflow around an Airfoil in the EGI Cloud CFD Support s OpenFOAM and UberCloud Containers enable efficient, effective, and easy access and use of MEET THE TEAM End-User/CFD
More informationParticle Image Velocimetry for Fluid Dynamics Measurements
Particle Image Velocimetry for Fluid Dynamics Measurements Lyes KADEM, Ph.D; Eng kadem@encs.concordia.ca Laboratory for Cardiovascular Fluid Dynamics MIE Concordia University Presentation - A bit of history
More informationA Knowledge Based Approach to Mesh Optimization in CFD Domain: ID Euler Code Example
A Knowledge Based Approach to Mesh Optimization in CFD Domain: ID Euler Code Example Tharini Santhanam, J.C. Browne, J. Kallinderis and D. Miranker Department of Computer Science The University of Texas
More informationNonoscillatory Central Schemes on Unstructured Triangulations for Hyperbolic Systems of Conservation Laws
Nonoscillatory Central Schemes on Unstructured Triangulations for Hyperbolic Systems of Conservation Laws Ivan Christov Bojan Popov Department of Mathematics, Texas A&M University, College Station, Texas
More informationAn Embedded Boundary Method with Adaptive Mesh Refinements
An Embedded Boundary Method with Adaptive Mesh Refinements Marcos Vanella and Elias Balaras 8 th World Congress on Computational Mechanics, WCCM8 5 th European Congress on Computational Methods in Applied
More informationCOMPUTATIONAL FLUID DYNAMICS ANALYSIS OF ORIFICE PLATE METERING SITUATIONS UNDER ABNORMAL CONFIGURATIONS
COMPUTATIONAL FLUID DYNAMICS ANALYSIS OF ORIFICE PLATE METERING SITUATIONS UNDER ABNORMAL CONFIGURATIONS Dr W. Malalasekera Version 3.0 August 2013 1 COMPUTATIONAL FLUID DYNAMICS ANALYSIS OF ORIFICE PLATE
More informationHomogenization and numerical Upscaling. Unsaturated flow and two-phase flow
Homogenization and numerical Upscaling Unsaturated flow and two-phase flow Insa Neuweiler Institute of Hydromechanics, University of Stuttgart Outline Block 1: Introduction and Repetition Homogenization
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 informationTransactions on Modelling and Simulation vol 20, 1998 WIT Press, ISSN X
Parallel indirect multipole BEM analysis of Stokes flow in a multiply connected domain M.S. Ingber*, A.A. Mammoli* & J.S. Warsa* "Department of Mechanical Engineering, University of New Mexico, Albuquerque,
More informationUsing a Single Rotating Reference Frame
Tutorial 9. Using a Single Rotating Reference Frame Introduction This tutorial considers the flow within a 2D, axisymmetric, co-rotating disk cavity system. Understanding the behavior of such flows is
More informationALE 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
More informationFinite Element Method. Chapter 7. Practical considerations in FEM modeling
Finite Element Method Chapter 7 Practical considerations in FEM modeling Finite Element Modeling General Consideration The following are some of the difficult tasks (or decisions) that face the engineer
More informationLevel Set Method in a Finite Element Setting
Level Set Method in a Finite Element Setting John Shopple University of California, San Diego November 6, 2007 Outline 1 Level Set Method 2 Solute-Solvent Model 3 Reinitialization 4 Conclusion Types of
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 informationhttp://miccom-center.org Topic: Continuum-Particle Simulation Software (COPSS-Hydrodynamics) Presenter: Jiyuan Li, The University of Chicago 2017 Summer School 1 What is Continuum-Particle Simulation?
More informationIntroduction to Multigrid and its Parallelization
Introduction to Multigrid and its Parallelization! Thomas D. Economon Lecture 14a May 28, 2014 Announcements 2 HW 1 & 2 have been returned. Any questions? Final projects are due June 11, 5 pm. If you are
More informationDevelopment of a Maxwell Equation Solver for Application to Two Fluid Plasma Models. C. Aberle, A. Hakim, and U. Shumlak
Development of a Maxwell Equation Solver for Application to Two Fluid Plasma Models C. Aberle, A. Hakim, and U. Shumlak Aerospace and Astronautics University of Washington, Seattle American Physical Society
More informationAsynchronous OpenCL/MPI numerical simulations of conservation laws
Asynchronous OpenCL/MPI numerical simulations of conservation laws Philippe HELLUY 1,3, Thomas STRUB 2. 1 IRMA, Université de Strasbourg, 2 AxesSim, 3 Inria Tonus, France IWOCL 2015, Stanford Conservation
More informationNumerical Methods for (Time-Dependent) HJ PDEs
Numerical Methods for (Time-Dependent) HJ PDEs Ian Mitchell Department of Computer Science The University of British Columbia research supported by National Science and Engineering Research Council of
More informationA methodology for the rigorous verification of plasma simulation codes
A methodology for the rigorous verification of plasma simulation codes Fabio Riva P. Ricci, C. Beadle, F.D. Halpern, S. Jolliet, J. Loizu, J. Morales, A. Mosetto, P. Paruta, C. Wersal École Polytechnique
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 informationIntroduction to ANSYS CFX
Workshop 03 Fluid flow around the NACA0012 Airfoil 16.0 Release Introduction to ANSYS CFX 2015 ANSYS, Inc. March 13, 2015 1 Release 16.0 Workshop Description: The flow simulated is an external aerodynamics
More informationAn Overview of Computational Fluid Dynamics
An Overview of Computational Fluid Dynamics Dr. Nor Azwadi bin Che Sidik Faculty of Mechanical Engineering Universiti Teknologi Malaysia INSPIRING CREATIVE AND INNOVATIVE MINDS 1 What is CFD? C computational
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 informationMath 690N - Final Report
Math 690N - Final Report Yuanhong Li May 05, 008 Accurate tracking of a discontinuous, thin and evolving turbulent flame front has been a challenging subject in modelling a premixed turbulent combustion.
More informationAirfoil Design Optimization Using Reduced Order Models Based on Proper Orthogonal Decomposition
Airfoil Design Optimization Using Reduced Order Models Based on Proper Orthogonal Decomposition.5.5.5.5.5.5.5..5.95.9.85.8.75.7 Patrick A. LeGresley and Juan J. Alonso Dept. of Aeronautics & Astronautics
More informationADVANCES IN ADAPTIVE METHODS IN COMPUTATIONAL FLUID MECHANICS. J. Tinsley Oden. Abstract
ADVANCES N ADAPTVE METHODS N COMPUTATONAL FLUD MECHANCS J. Tinsley Oden Texas nstitute for Computational Mechanics The University of Texas at Austin Austin, Texas 78712 Abstract Recent developments in
More informationSmoothers. < interactive example > Partial Differential Equations Numerical Methods for PDEs Sparse Linear Systems
Smoothers Partial Differential Equations Disappointing convergence rates observed for stationary iterative methods are asymptotic Much better progress may be made initially before eventually settling into
More informationA MULTI-DOMAIN ALE ALGORITHM FOR SIMULATING FLOWS INSIDE FREE-PISTON DRIVEN HYPERSONIC TEST FACILITIES
A MULTI-DOMAIN ALE ALGORITHM FOR SIMULATING FLOWS INSIDE FREE-PISTON DRIVEN HYPERSONIC TEST FACILITIES Khalil Bensassi, and Herman Deconinck Von Karman Institute for Fluid Dynamics Aeronautics & Aerospace
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 informationA Direct Simulation-Based Study of Radiance in a Dynamic Ocean
A Direct Simulation-Based Study of Radiance in a Dynamic Ocean Lian Shen Department of Civil Engineering Johns Hopkins University Baltimore, MD 21218 phone: (410) 516-5033 fax: (410) 516-7473 email: LianShen@jhu.edu
More informationApplication of CFD to Industrial Safety Studies (with Prediction Accuracy and Error estimations)
School of Mechanical Aerospace and Civil Engineering University of Manchester First Year Transfer Report Application of CFD to Industrial Safety Studies (with Prediction Accuracy and Error estimations)
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 informationUnstructured Mesh Generation for Implicit Moving Geometries and Level Set Applications
Unstructured Mesh Generation for Implicit Moving Geometries and Level Set Applications Per-Olof Persson (persson@mit.edu) Department of Mathematics Massachusetts Institute of Technology http://www.mit.edu/
More informationSimulating Smoke with an Octree Data Structure and Ray Marching
Simulating Smoke with an Octree Data Structure and Ray Marching Edward Eisenberger Maria Montenegro Abstract We present a method for simulating and rendering smoke using an Octree data structure and Monte
More informationFinite Element Analysis Prof. Dr. B. N. Rao Department of Civil Engineering Indian Institute of Technology, Madras. Lecture - 36
Finite Element Analysis Prof. Dr. B. N. Rao Department of Civil Engineering Indian Institute of Technology, Madras Lecture - 36 In last class, we have derived element equations for two d elasticity problems
More informationScientific Visualization. CSC 7443: Scientific Information Visualization
Scientific Visualization Scientific Datasets Gaining insight into scientific data by representing the data by computer graphics Scientific data sources Computation Real material simulation/modeling (e.g.,
More informationThe WENO Method in the Context of Earlier Methods To approximate, in a physically correct way, [3] the solution to a conservation law of the form u t
An implicit WENO scheme for steady-state computation of scalar hyperbolic equations Sigal Gottlieb Mathematics Department University of Massachusetts at Dartmouth 85 Old Westport Road North Dartmouth,
More informationUsing the Eulerian Multiphase Model for Granular Flow
Tutorial 21. Using the Eulerian Multiphase Model for Granular Flow Introduction Mixing tanks are used to maintain solid particles or droplets of heavy fluids in suspension. Mixing may be required to enhance
More informationNumerical Analysis of Shock Tube Problem by using TVD and ACM Schemes
Numerical Analysis of Shock Tube Problem by using TVD and Schemes Dr. Mukkarum Husain, Dr. M. Nauman Qureshi, Syed Zaid Hasany IST Karachi, Email: mrmukkarum@yahoo.com Abstract Computational Fluid Dynamics
More informationNon-Newtonian Transitional Flow in an Eccentric Annulus
Tutorial 8. Non-Newtonian Transitional Flow in an Eccentric Annulus Introduction The purpose of this tutorial is to illustrate the setup and solution of a 3D, turbulent flow of a non-newtonian fluid. Turbulent
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 informationLecture 1.1 Introduction to Fluid Dynamics
Lecture 1.1 Introduction to Fluid Dynamics 1 Introduction A thorough study of the laws of fluid mechanics is necessary to understand the fluid motion within the turbomachinery components. In this introductory
More informationComputational Modeling and Simulation of the Human Duodenum
Computational Modeling and Simulation of the Human Duodenum Bostjan Hari 1, Serafim Bakalis 1, Peter Fryer 1 1 The University of Birmingham, School of Chemical Engineering, Edgbaston, Birmingham, United
More informationModule 1: Introduction to Finite Difference Method and Fundamentals of CFD Lecture 13: The Lecture deals with:
The Lecture deals with: Some more Suggestions for Improvement of Discretization Schemes Some Non-Trivial Problems with Discretized Equations file:///d /chitra/nptel_phase2/mechanical/cfd/lecture13/13_1.htm[6/20/2012
More informationCloud-based simulation of plasma sources for surface treatment
Cloud-based simulation of plasma sources for surface treatment Using the PlasmaSolve Simulation Suite (P3S) Adam Obrusnik, Petr Zikan June 7, 2018 Outline 1. About PlasmaSolve 2. PlasmaSolve Simulation
More information1.2 Numerical Solutions of Flow Problems
1.2 Numerical Solutions of Flow Problems DIFFERENTIAL EQUATIONS OF MOTION FOR A SIMPLIFIED FLOW PROBLEM Continuity equation for incompressible flow: 0 Momentum (Navier-Stokes) equations for a Newtonian
More informationA STUDY ON THE UNSTEADY AERODYNAMICS OF PROJECTILES IN OVERTAKING BLAST FLOWFIELDS
HEFAT2012 9 th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics 16 18 July 2012 Malta A STUDY ON THE UNSTEADY AERODYNAMICS OF PROJECTILES IN OVERTAKING BLAST FLOWFIELDS Muthukumaran.C.K.
More informationMid-Year Report. Discontinuous Galerkin Euler Equation Solver. Friday, December 14, Andrey Andreyev. Advisor: Dr.
Mid-Year Report Discontinuous Galerkin Euler Equation Solver Friday, December 14, 2012 Andrey Andreyev Advisor: Dr. James Baeder Abstract: The focus of this effort is to produce a two dimensional inviscid,
More informationNumerical and theoretical analysis of shock waves interaction and reflection
Fluid Structure Interaction and Moving Boundary Problems IV 299 Numerical and theoretical analysis of shock waves interaction and reflection K. Alhussan Space Research Institute, King Abdulaziz City for
More informationLarge Eddy Simulation of Flow over a Backward Facing Step using Fire Dynamics Simulator (FDS)
The 14 th Asian Congress of Fluid Mechanics - 14ACFM October 15-19, 2013; Hanoi and Halong, Vietnam Large Eddy Simulation of Flow over a Backward Facing Step using Fire Dynamics Simulator (FDS) Md. Mahfuz
More informationThree Dimensional Numerical Simulation of Turbulent Flow Over Spillways
Three Dimensional Numerical Simulation of Turbulent Flow Over Spillways Latif Bouhadji ASL-AQFlow Inc., Sidney, British Columbia, Canada Email: lbouhadji@aslenv.com ABSTRACT Turbulent flows over a spillway
More informationParallelization study of a VOF/Navier-Stokes model for 3D unstructured staggered meshes
Parallelization study of a VOF/Navier-Stokes model for 3D unstructured staggered meshes L. Jofre, O. Lehmkuhl, R. Borrell, J. Castro and A. Oliva Corresponding author: cttc@cttc.upc.edu Centre Tecnològic
More informationIntroduction to the immersed boundary method
Introduction to the immersed boundary method Motivation. Hydrodynamics and boundary conditions The incompressible Navier-Stokes equations, ( ) u ρ + (u )u = p + ρν 2 u + f, () t are partial differential
More informationELECTRON DOSE KERNELS TO ACCOUNT FOR SECONDARY PARTICLE TRANSPORT IN DETERMINISTIC SIMULATIONS
Computational Medical Physics Working Group Workshop II, Sep 30 Oct 3, 2007 University of Florida (UF), Gainesville, Florida USA on CD-ROM, American Nuclear Society, LaGrange Park, IL (2007) ELECTRON DOSE
More informationMaterials Modelling MPhil
Materials Modelling MPhil COURSE MP5: MESOSCALE AND MULTISCALE MODELLING COMPUTING CLASS 1 31/1/2007 14:00-16:00 Dissipative particle dynamics using Materials Studio 4.0 1 Aims and objectives Dissipative
More informationDirections: 1) Delete this text box 2) Insert desired picture here
Directions: 1) Delete this text box 2) Insert desired picture here Multi-Disciplinary Applications using Overset Grid Technology in STAR-CCM+ CD-adapco Dmitry Pinaev, Frank Schäfer, Eberhard Schreck Outline
More informationSoftware and Performance Engineering for numerical codes on GPU clusters
Software and Performance Engineering for numerical codes on GPU clusters H. Köstler International Workshop of GPU Solutions to Multiscale Problems in Science and Engineering Harbin, China 28.7.2010 2 3
More informationStress analysis of Camshaft by using ANSYS Software
Stress analysis of Camshaft by using ANSYS Software Samta Jain, Mr. Vikas Bansal Rajasthan Technical University, kota (Rajasathan), India Abstract This paper presents the modeling and static structural
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 informationNumerical study of swimming of an organism in a viscous fluid in a channel
ISSN 1 746-7233, England, UK World Journal of Modelling and Simulation Vol. 14 (2018) No. 2, pp. 100-107 Numerical study of swimming of an organism in a viscous fluid in a channel Ranjith Maniyeri 1 *,
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 informationVelocity and Concentration Properties of Porous Medium in a Microfluidic Device
Velocity and Concentration Properties of Porous Medium in a Microfluidic Device Rachel Freeman Department of Chemical Engineering University of Washington ChemE 499 Undergraduate Research December 14,
More information