Introduction to the eclipse ide and 1 d heat diffusion
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Introduction to The Eclipse IDE and 1-D Heat Diffusion. Dr. Jennifer Parham-Mocello. What is an IDE?. IDE – Integrated Development Environment Software application providing conveniences to computer programmers for software development.

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Introduction to The Eclipse IDE and 1-D Heat Diffusion

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Introduction to the eclipse ide and 1 d heat diffusion

Introduction to The Eclipse IDE and 1-D Heat Diffusion

Dr. Jennifer Parham-Mocello


What is an ide

What is an IDE?

  • IDE – Integrated Development Environment

  • Software application providing conveniences to computer programmers for software development.

  • Consists of editor, compiler/interpreter, building tools, and a graphical debugger.

Heat Diffusion / Finite Difference Methods


Eclipse

Eclipse

  • Java, C/C++, and PHP IDE

  • Uses Java Runtime Environment (JRE)

    • Install JRE/JDK - http://www.oracle.com/technetwork/java/index.html

  • Need C/C++ compiler

    • Install Wascana (Windows version) http://www.eclipselabs.org/p/wascana

Heat Diffusion / Finite Difference Methods


Using eclipse

Using Eclipse

  • Example – Open HelloWorld C++ project

    • File -> New -> C++ Project

    • Enter Project Name

  • Building/Compiling Projects

    • Project -> Build All

    • Run -> Run

  • Console

Heat Diffusion / Finite Difference Methods


Heat diffusion

Heat Diffusion

Heat Diffusion / Finite Difference Methods


Introduction to the eclipse ide and 1 d heat diffusion

Heat Diffusion Equation

  • Describes the distribution of heat (or variation in temperature) in a given region over time.

  • For a function u(x, t) of one spatial variables(x) and the time variable t, the heat diffusion equation is:

1D

or

1D

Material Parameters – thermal conductivity (k), specific heat (c), density ()

Heat Diffusion / Finite Difference Methods


Conceptual and theoretical basis

Conceptual and theoretical basis

  • Conservation of mass, energy, momentum, etc.

  • Rate of flow in - Rate of flow out = Rate of heat storage

2D

1D

3D

Heat Diffusion / Finite Difference Methods


Example 1d heat diffusion problem

Example 1D Heat Diffusion Problem

Wire with perfect insulation, except at ends

x=4.0

x=0.0

Boundary

Conditions

Physical Parameters

Initial

Conditions

Heat Diffusion / Finite Difference Methods


Outline of solution

Outline of Solution

  • Discretization (spatial and temporal)

  • Transformation of theoretical equations to approximate algebraic form

  • Solution of algebraic equations

Heat Diffusion / Finite Difference Methods


Discretization

Discretization

  • Spatial - Partition into equally-spaced nodes

u0

u1

u2

u3

Temporal - Decide on time stepping parameters

x=0.33

x=0.67

x=1.0

x=0.0

Let to = 0.0, tn = 10.0, and Dt = 0.1

Heat Diffusion / Finite Difference Methods


Approximate theoretical with algebra

Approximate Theoretical with Algebra

Finite difference approximations for

first and second derivatives

u0

u1

ui-1

ui

ui+1

un-1

un

Heat Diffusion / Finite Difference Methods


Approximation

Approximation

Heat Diffusion / Finite Difference Methods


Algorithm

Algorithm

fort=0,tn

for each node, i

predict ut+Dt

endfor

endfor

  • Predicting ut+Dt at each node

    • Explicit solution

    • Implicit solution (system of equations)

Heat Diffusion / Finite Difference Methods


Explicit solution

Explicit Solution

Heat Diffusion / Finite Difference Methods


Simulation explicit solution

Simulation (Explicit Solution)

Physical Parameters

u0

u1

u2

u3

Boundary

Conditions

Initial

Conditions

Heat Diffusion / Finite Difference Methods


Extension

Extension

  • Two Dimensions

u i,j+1

u i,j

u i-1,j

u i+1,j

u i,j-1

Heat Diffusion / Finite Difference Methods


Implement 1 d heat diffusion

Implement 1-D Heat Diffusion

  • Open New C++ Project

  • Name the Project

  • Open New C++ source code file

    • File -> New -> Source File

  • Name C++ File (remember extension, .C, .c++, .cpp)

Heat Diffusion / Finite Difference Methods


Extras

EXTRAS

Heat Diffusion / Finite Difference Methods


Shorthand notations

Shorthand Notations

  • Gradient (“Del”) Operator

Heat Diffusion / Finite Difference Methods


Introduction to the eclipse ide and 1 d heat diffusion

  • Divergence (Gradient of a vector field)

Heat Diffusion / Finite Difference Methods


Introduction to the eclipse ide and 1 d heat diffusion

  • Laplacian Operator

Heat Diffusion / Finite Difference Methods


Introduction to the eclipse ide and 1 d heat diffusion

  • Heat Diffusion Equation - rewritten

  • LHS represents spatial variations

  • RHS represents temporal variation

Heat Diffusion / Finite Difference Methods


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