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3.1 Introduction A generic transport equation ∂ρu j φ ∂x j = ∂ ∂x j (Γ ∂φ ∂x j ) + q φ . (3.1 F&P ) In Cartesian Coordinates, ∂ρuφ ∂x + ∂ρvφ ∂y + ∂ρwφ ∂z = ∂ ∂x (Γ∂φ ∂x ) + ∂ ∂y (Γ∂φ ∂y ) + ∂ ∂z (Γ∂φ ∂z ) + q φ. 3
3.1 Introduction A generic transport equation ∂ρu j φ ∂x j = ∂ ∂x j (Γ ∂φ ∂x j ) + q φ . (3.1 F&P ) In Cartesian Coordinates, ∂ρuφ ∂x + ∂ρvφ ∂y + ∂ρwφ ∂z = ∂ ∂x (Γ∂φ ∂x ) + ∂ ∂y (Γ∂φ ∂y ) + ∂ ∂z (Γ∂φ ∂z ) + q φ. Simplifications Convection Terms Diffusion Terms Source Term Unsteady Term (Ch. 6) 3
Page 1 and 2: ES440/ES911: CFD Chapter 3. Finite
Page 3: 3.1 Introduction A generic transpor
Page 7 and 8: 3.2 - 1D Discretisation Divide the
Page 9 and 10: 3.2 Basic Concept - Cont’d Unifor
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
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First Order Accuracy: O(∆x) FORWA
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Second Order Accuracy: O(∆x 2 ) C
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Second Order Accuracy: O(∆x 2 ) C
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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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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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Solution to 1D Matrix Equations Dir
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Example of First-Order ODE Heat Tra
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3.11 Example The generic transport
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Slides - School of Engineering - University of Warwick

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