AE/ME 339 Computational Fluid Dynamics (CFD) K. M. Isaac Professor of Aerospace Engineering.

Slides:

Advertisements

Similar presentations

Finite Difference Discretization of Hyperbolic Equations: Linear Problems Lectures 8, 9 and 10.

Advertisements

Chapter 8 Elliptic Equation.

PART 7 Ordinary Differential Equations ODEs

ECE602 BME I Partial Differential Equations in Biomedical Engineering.

PARTIAL DIFFERENTIAL EQUATIONS

Lecture 34 - Ordinary Differential Equations - BVP CVEN 302 November 28, 2001.

Computational Fluid Dynamics I PIW Numerical Methods for Parabolic Equations Instructor: Hong G. Im University of Michigan Fall 2005.

Partial differential equations Function depends on two or more independent variables This is a very simple one - there are many more complicated ones.

Numerical Methods for Partial Differential Equations

CISE301: Numerical Methods Topic 9 Partial Differential Equations (PDEs) Lectures KFUPM (Term 101) Section 04 Read & CISE301_Topic9.

SE301: Numerical Methods Topic 9 Partial Differential Equations (PDEs) Lectures KFUPM Read & CISE301_Topic9 KFUPM.

Numerical methods for PDEs PDEs are mathematical models for –Physical Phenomena Heat transfer Wave motion.

© 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the.

CHAPTER 7 NON-LINEAR CONDUCTION PROBLEMS

1 EEE 431 Computational Methods in Electrodynamics Lecture 4 By Dr. Rasime Uyguroglu

Math 3120 Differential Equations with Boundary Value Problems

7. Introduction to the numerical integration of PDE. As an example, we consider the following PDE with one variable; Finite difference method is one of.

Engineering Analysis – Computational Fluid Dynamics –

Engineering Analysis – Computational Fluid Dynamics –

AE/ME 339 Computational Fluid Dynamics (CFD) K. M. Isaac Professor of Aerospace Engineering Introduction and Scope.

Engineering Analysis – Computational Fluid Dynamics –

Circuits Theory Examples Newton-Raphson Method. Formula for one-dimensional case: Series of successive solutions: If the iteration process is converged,

CIS/ME 794Y A Case Study in Computational Science & Engineering 2-D conservation of momentum (contd.) Or, in cartesian tensor notation, Where repeated.

Partial Derivatives bounded domain Its boundary denoted by

Partial Derivatives Example: Find If solution: Partial Derivatives Example: Find If solution: gradient grad(u) = gradient.

Solving Partial Differential Equation Numerically Pertemuan 13 Matakuliah: S0262-Analisis Numerik Tahun: 2010.

1 Spring 2003 Prof. Tim Warburton MA557/MA578/CS557 Lecture 32.

Ordinary Differential Equations (ODEs). Objectives of Topic  Solve Ordinary Differential Equations (ODEs).  Appreciate the importance of numerical methods.

Differential Equations

Computational Fluid Dynamics Lecture II Numerical Methods and Criteria for CFD Dr. Ugur GUVEN Professor of Aerospace Engineering.

Finite Difference Methods

Applications of Lattice Methods

Chapter 2. Mathematical Expression of Conduction

ME/AE 339 Computational Fluid Dynamics K. M. Isaac Topic1_ODE

AE/ME 339 Computational Fluid Dynamics (CFD) K. M. Isaac 11/13/2018

AE/ME 339 Computational Fluid Dynamics (CFD) K. M. Isaac 11/15/2018

Partial Differential Equations

Finite Difference Method

ME/AE 339 Computational Fluid Dynamics K. M. Isaac Topic2_PDE

Topic 6 FluidFlowEquations_Introduction

AE/ME 339 Computational Fluid Dynamics (CFD) K. M. Isaac 12/3/2018

Topic 3 Discretization of PDE

topic13_grid_generation

AE/ME 339 Computational Fluid Dynamics (CFD) K. M. Isaac

topic8_NS_vectorForm_F02

topic13_grid_generation

topic13_grid_generation

topic4: Implicit method, Stability, ADI method

topic4: Implicit method, Stability, ADI method

Topic 3 Discretization of PDE

topic16_cylinder_flow_relaxation

Topic 5 NavierStokes Equations

topic11_shocktube_problem

topic4: Implicit method, Stability, ADI method

Topic 6 NavierStokes Equations

AE/ME 339 Computational Fluid Dynamics (CFD) K. M. Isaac 2/28/2019

Topic9_Pressure_Correction

topic8_NS_vectorForm_F02

topic11_shocktube_problem

AE/ME 339 Computational Fluid Dynamics (CFD) K. M. Isaac 4/30/2019

Topic 8 Pressure Correction

topic4: Implicit method, Stability, ADI method

AE/ME 339 Computational Fluid Dynamics (CFD) K. M. Isaac 7/24/2019

AE/ME 339 Computational Fluid Dynamics (CFD) K. M. Isaac July 25, 2019

topic18_shock_tube_flow

AE/ME 339 Computational Fluid Dynamics (CFD) K. M. Isaac

AE/ME 339 Computational Fluid Dynamics (CFD) K. M. Isaac

Topic 3 Discretization of PDE

AE/ME 339 Computational Fluid Dynamics (CFD) K. M. Isaac

Presentation transcript:

AE/ME 339 Computational Fluid Dynamics (CFD) K. M. Isaac Professor of Aerospace Engineering

Computational Fluid Dynamics (AE/ME 339) K. M. Isaac MAEEM Dept., UMR Quiz 1

Computational Fluid Dynamics (AE/ME 339) K. M. Isaac MAEEM Dept., UMR Test 1 topics Modeling of fluid flow in a constant area pipe with heat addition and/or friction Resulting ODE and its numerical solution use of Taylor series to approximate functions and their derivatives Numerical solution of initial value problems using R-K

Computational Fluid Dynamics (AE/ME 339) K. M. Isaac MAEEM Dept., UMR Unsteady 1D heat conduction equation Nature of the equation Discretization of derivatives using Taylor series Taylor series in more than one independent variable An example of a non-linear PDE from fluid mechanics Compact notation for CD approximation for 2 nd derivative

Computational Fluid Dynamics (AE/ME 339) K. M. Isaac MAEEM Dept., UMR Explicit method of solution Problem setup Initial and boundary conditions von Neumann stability analysis for explicit and implicit schemes Solution procedure for implicit method using Gauss elimination Crank-Nicolson method. Stability of C-N ADI method Step-by-step implementation of ADI

Computational Fluid Dynamics (AE/ME 339) K. M. Isaac MAEEM Dept., UMR Types of boundary conditions Dirichlet, Neumann and mixed BC Non-linear PDEs. Linearization techniques

Computational Fluid Dynamics (AE/ME 339) K. M. Isaac MAEEM Dept., UMR