Length Learning Objectives Learning Objectives Assessment

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August Hardy
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1 Universidade Federal Fluminense PGMEC Course: Advanced Computational Fluid Dynamics Coordinator: Vassilis Theofilis Academic Year: 2018, 2 nd Semester Length: 60hrs (48hrs classroom and 12hrs tutorials) 180hrs total student time Learning Objectives (mandatory): Extend knowledge on prototype (hyperbolic, parabolic, elliptic) equations acquired in previous courses to the equations of Fluid Mechanics. Mesh generation using the Open Source GMSH meshing s/w Familiarization with three CFD open source codes, OpenFOAM (finite volumes), nek5000 (spectral element, incompressible) and nektar++ (spectral element, incompressible and Discontinuous Galerkin, compressible) Write, debug and run: o Two incompressible NS codes for the solution of two-dimensional problems, with: A splitting scheme in primitive variables, using finite-difference spatial discretization Solution of the vorticity transport equation, using spectral collocation spatial discretization o Two compressible NS codes for the solution of one- and two-dimensional problems Burgers equation in two spatial dimensions Interaction of a vortex with a shock Learning Objectives (optional): Learn basic parallelization techniques using OpenMP (UFF) and MPI (U of Liverpool). Apply to: o Solve large linear systems of equations, AX=B, by distributing matrix A o Parallelize own existing codes, identifying performance bottlenecks Assessment: Average mark of four courseworks performed during the course Coursework 1: Solution of the ODE f + 2 f = 0, f(0) = 3 o Discretize using FD-2, FD-4, Padé and CGL using LAPACK (mandatory) Coursework 2: Solution of the two-dimensional Poisson equation in a unit square o Discretize and solve the linear PDE as a linear system and as an eigenvalue problem, o using finite difference and spectral methods. Solve Serial (using Fortran and Lapack, mandatory) Parallel using up to 40 cores (using ScaLAPACK, optional) o Compare results with analytical solution and discuss convergence of FD vs spectral methods

2 Coursework 3: Solutions using OpenFOAM o Solve the laminar compressible flow on a flat plate, inviscid supersonic flow over a diamond-shaped airfoil and turbulent subsonic flow on an airfoil o Use gmsh to create a mesh (.geo and.msh), convert gmsh.msh file to be read by OpenFOAM and run simulations in OF o Compare numerical results with theory: Lees & Reshotko (laminar flat plate) Prandtl-Meyer (diamond-shaped airfoil) Coursework 4: Solve the incompressible NS for the 2D lid-driven cavity o Use primitive variables, a pressure correction scheme and discretize using FD-4 and CGL spatial discretization, using a collocated scheme o Solve the stream function / vorticity transport equation Assets: Student s own laptop Computing cluster at UFF (OpenMP) One node of the computing cluster Barkla at the Univ. of Liverpool o (40 CPUs, 384 GB shared memory) o pre-installed OpenFOAM, nek5000 and nektar++ software o Job scheduling system Bibliography: RH Pletcher, JC Tannehill, DA Anderson (2013) Computational Fluid Mechanics and Heat Transfer, (3 rd Edition), CRC Press Online Documentation o OpenFOAM ( o nek5000 ( o nektar++ ( Material distributed in class

3 Schedule: Taught Classes (UFF): o Aug (V Theofilis): Numerical solution of linear systems, eigenvalue problems and parallelization (12hrs) Monday, August 20 o Classification of PDEs o Intro to Finite Difference (FD) and Spectral Methods o Convergence and presentation of results o Intro to gnuplot Tuesday, August 21 o Intro to LAPACK o Numerical solution of linear and nonlinear systems, linear and nonlinear eigenvalue problems using FD and the Chebyshev Gauss Lobatto spectral method Wednesday, August 22 o Intro to Parallel Computation and MPI o Intro to ScaLAPACK Thursday, August 23 Friday, August 24 o Assignment and discussion of Courseworks 1 and 2 o Sept (Leonardo Alves): Introduction to GMSH and OpenFOAM (12hrs) Monday, Sept 17 o Intro to GMSH. Examples: Flat-plate boundary layer 2D Lid-driven cavity, uniform and wall-refined mesh Tuesday, Sept 18 o Intro to OF o Intro to Paraview o Solution of laminar flows using OF: PPF, Couette, 2D Lid-driven Cavity, Blasius Wednesday, Sept 19 o Solution of turbulent and compressible flows using OF: Flow around a NACA0012 airfoil Flow in a compression ramp Thursday, Sept 20 Friday, Sept 21 o Assignment and discussion of Courseworks 1 and 2

4 o Oct 29 Nov 2 (V Theofilis): Splitting methods (6hrs) and the stream-function / vorticity transport equations (6hrs) for the solution of the 2D incompressible Navier-Stokes equations Monday, Oct 29 o Primitive variables and pressure correction schemes o Boundary condition based on the pressure Poisson equation Tuesday, Oct 30 o Temporal discretization using Runge-Kutta explicit schemes The Spalart, Moser, Rogers semi-implicit scheme o Spatial discretization using FD-4 and CGL Wednesday, Oct 31 o Stream function / vorticity transport equations o The Moin-Kim algorithm Thursday, Nov 1 Friday, Nov 2 o Assignment and discussion of Coursework 4 o November (Leonardo Alves): Introduction to nektar++ and nek5000 (12hrs) Monday, Nov 26 o Intro to nektar++. Meshing using GMSH. Examples: 2D Lid-driven cavity, uniform and wall-refined mesh Tuesday, Nov 27 o Laminar compressible flows using nektar++: Flow around a NACA0012 airfoil Flow in a compression ramp Comparisons with OpenFOAM Wednesday, Nov 28 o Intro to nek5000. Examples: 3D Lid-driven cavity, uniform mesh Thursday, Nov 29 Friday, Nov 30 o Discussion of Coursework 3 o December Intro to compressible Euler and NS (8hrs) and Revision (4hrs): Monday, Dec 17 o Basics of spatial discretization for compressible Euler and NS Finite differences Finite volumes

5 Spectral collocation Discontinuous Galerkin Tuesday, Dec 18 o Laminar compressible flows examples using own-written s/w: 1D and 2D Burgers equation 2D Vortex/shock interaction Wednesday, Dec 19 o Revision Day Online Tutorials (Skype name: v.theofilis): o Week 35: 2pm 4 pm (Central European Time) o Week 39: 2pm 4 pm (Central European Time) o Week 45: 2pm 4 pm (Central European Time)

Computational Fluid Dynamics-1(CFDI)

بسمه تعالی درس دینامیک سیالات محاسباتی 1 دوره کارشناسی ارشد دانشکده مهندسی مکانیک دانشگاه صنعتی خواجه نصیر الدین طوسی Computational Fluid Dynamics-1(CFDI) Course outlines: Part I A brief introduction to