l6 - Lecture 6: The Diffusion Equation A First Look 1 Last...

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1 Lecture 6: The Diffusion Equation A First Look
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2 Last Time… We completed an overview of the numerical discretization and solution process » Solution of linear algebraic set » Properties of discretization and path to solution – Accuracy, consistency, convergence, stability
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3 This Time… We will Apply the finite volume scheme to the steady diffusion equation on Cartesian structured meshes Examine the properties of the resulting discretization Describe how to discretize boundary conditions
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4 • Consider steady diffusion with a source term: Here • Integrate over control volume to yield 2D Steady Diffusion
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5 2D Steady Diffusion Apply divergence theorem to yield
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6 Writing integral over control volume: •Compactly: Discrete Flux Balance
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7 Discrete Flux Balance (cont’d) Area vectors given by: Fluxes given by
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8 Discretization Assume varies linearly between cell centroids Note: » Symmetry of (P, E ) and (P,W) in flux expression » Opposite signs on (P,E) and (P,W) terms
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l6 - Lecture 6: The Diffusion Equation A First Look 1 Last...

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