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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
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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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Lecture 11 –Finite Volume Method 37
(the matrix is diagonally dominant)
