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Introduction to Computational Fluid Dynamics
Lecture 11 –Finite Volume Method 1
FINITE VOLUME METHOD (Jayathi Y. Murthy, Numerical Methods in Heat, Mass, and Momentum Transfer, Purdue University, Spring 2002)
Mesh terminology and types
(structured mesh - every interior vertex in the domain is connected to the same number of neighbour
vertices)
Introduction to Computational Fluid Dynamics
Lecture 11 –Finite Volume Method 2
(non-conformal mesh - the vertices of a cell or element may fall on the faces of neighboring cells or
elements)
Introduction to Computational Fluid Dynamics
Lecture 11 –Finite Volume Method 3
.
Introduction to Computational Fluid Dynamics
Lecture 11 –Finite Volume Method 4
Finite Volume Discretization
Consider the 1D diffusion equation
Introduction to Computational Fluid Dynamics
Lecture 11 –Finite Volume Method 5
on the following control volume:
over
Introduction to Computational Fluid Dynamics
Lecture 11 –Finite Volume Method 6
One obtain
Introduction to Computational Fluid Dynamics
Lecture 11 –Finite Volume Method 7
Similar equation may be derived for all cells in the domain, yielding a set of
algebraic equations, as before; these may be solved using a variety of direct or
iterative methods.
Introduction to Computational Fluid Dynamics
Lecture 11 –Finite Volume Method 8
Introduction to Computational Fluid Dynamics
Lecture 11 –Finite Volume Method 9
Introduction to Computational Fluid Dynamics
Lecture 11 –Finite Volume Method 10
Introduction to Computational Fluid Dynamics
Lecture 11 –Finite Volume Method 11
Introduction to Computational Fluid Dynamics
Lecture 11 –Finite Volume Method 12
Introduction to Computational Fluid Dynamics
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Introduction to Computational Fluid Dynamics
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Introduction to Computational Fluid Dynamics
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Introduction to Computational Fluid Dynamics
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Introduction to Computational Fluid Dynamics
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Introduction to Computational Fluid Dynamics
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Introduction to Computational Fluid Dynamics
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Introduction to Computational Fluid Dynamics
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Introduction to Computational Fluid Dynamics
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Introduction to Computational Fluid Dynamics
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Introduction to Computational Fluid Dynamics
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Introduction to Computational Fluid Dynamics
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Introduction to Computational Fluid Dynamics
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Introduction to Computational Fluid Dynamics
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Introduction to Computational Fluid Dynamics
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Introduction to Computational Fluid Dynamics
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Introduction to Computational Fluid Dynamics
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Introduction to Computational Fluid Dynamics
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Introduction to Computational Fluid Dynamics
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Introduction to Computational Fluid Dynamics
Lecture 11 –Finite Volume Method 37
(the matrix is diagonally dominant)
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