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3.2 - Discretisation Each node has one unknown variable associated with it. 1D: f 1 , f 2 , f 3 , . . . , f i−1 , f i , f i+1 , . . . , f N−2 , f N−1 , f N . 2D: f 1,1 , f 2,1 , f 3,1 , . . . , f i−1,j , f i,j , f i+1,j , . . . , f N−1,N , f N,N . 3D: f 1,1,1 , f 2,1,1 , f 3,1,1 , . . . , f i−1,j,k , f i,j,k , f i+1,j,k , . . . , f N,N,N . 6
3.2 Basic Concept - Cont’d Uniform vs. Non-uniform grids 7
Page 1 and 2: ES440/ES911: CFD Chapter 3. Finite
Page 3 and 4: 3.1 Introduction A generic transpor
Page 5 and 6: 3.1 Introduction A generic transpor
Page 7: 3.2 - 1D Discretisation Divide the
Page 11 and 12: 3.2 Basic Concept - Cont’d Each n
Page 13 and 14: 3.2 Basic Concept - Cont’d Each n
Page 15 and 16: 3.2 Basic Concept - Cont’d A gene
Page 17 and 18: 3.2 - Finite Difference Approximati
Page 19 and 20: 3.2 - Finite Difference Approximati
Page 21 and 22: Taylor Series Expansion Taylor Seri
Page 23 and 24: 3.3 - Forward Difference: ∂f ∂x
Page 25 and 26: 3.3 - Forward Difference: ∂f ∂x
Page 27 and 28: 3.3 - Forward Difference - Cont’d
Page 29 and 30: 3.3 - Backward Difference: ∂f ∂
Page 31 and 32: 3.3 - Backward Difference - Cont’
Page 33 and 34: 3.3 - Central Difference: ∂f ∂x
Page 35 and 36: 3.3 - Truncation Errors Numerically
Page 37 and 38: 3.3 - Fourth Order Accuracy In gene
Page 39 and 40: 3.3 - Fourth Order Accuracy - Cont
Page 41 and 42: 3.3 - Higher Order Accuracy Second-
Page 43 and 44: 3.3 - Higher Order Accuracy Second-
Page 45 and 46: 3.3 - High Order Accuracy - Cont’
Page 47 and 48: 3.4 Second Order Derivative: ∂2 f
Page 49 and 50: 3.4 - Higher Order Accuracy: O(∆x
Page 51 and 52: 3.4 Third Order Derivative: ∂3 f
Page 53 and 54: 3.4 Third Order Derivative: ∂3 f
Page 55 and 56: First Order Accuracy: O(∆x) FORWA
Page 57 and 58: Second Order Accuracy: O(∆x 2 ) C
Page 59 and 60:
Second Order Accuracy: O(∆x 2 ) C
Page 61 and 62:
Fourth Order Accuracy: O(∆x 4 ) C
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Fourth Order Accuracy: O(∆x 4 ) C
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Finite Difference Method for Ellipt
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Finite Difference Method for Ellipt
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One-Dimensional FDM Elliptic PDE: L
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One-Dimensional FDM Elliptic PDE: L
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One-Dimensional FDM ∂ 2 u ∂x 2
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3.8 Algebraic Equation System u 1
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3.8 - Linear Algebraic Equation Fin
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3.8 - Matrix Equations - Cont’d A
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Page 83 and 84:
1-D Navier-Stokes Equation Elliptic
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1-D Navier-Stokes Equation Elliptic
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One-Dimensional FDM 1 Re ∂ 2 u
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3.8 Algebraic Equation System u 1
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3.8 - Matrix Equations for 1D FDM T
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TDMA: Thomas Algorithm An upper tri
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Page 97 and 98:
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Solution to 1D Matrix Equations Dir
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Example of First-Order ODE Heat Tra
Page 103 and 104:
3.11 Example The generic transport
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Slides - School of Engineering - University of Warwick

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