l7 - Lecture 7: A First Look at the Diffusion Equation...

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1 Lecture 7: A First Look at the Diffusion Equation (cont’d)
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2 Last Time… We looked at the 2D diffusion equation on Cartesian structured meshes. We Integrated diffusion equation on CV Applied divergence theorem to obtain flux balance Made linear profile assumption Derived discrete algebraic equation
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3 This Time… We will: complete discussion of the properties of the discrete equations complete discretization of boundary conditions » Dirichlet, Neumann, mixed (Robbins)
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4 Final Discrete Equation P N S E W
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5 Comments Discrete equation reflects balance of flux*area with generation inside control volume As in 1-D case, we need fluxes at cell faces These are written in terms of cell-centroid values using profile assumptions.
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6 Comments (cont’d) Formulation is conservative: Discrete equation was derived by enforcing conservation. Fluxes balance source term regardless of mesh density For a structured mesh, each point P is coupled to its four nearest neighbors. Corner points do not enter the formulation.
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This note was uploaded on 12/29/2011 for the course ME 608 taught by Professor Na during the Fall '10 term at Purdue.

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l7 - Lecture 7: A First Look at the Diffusion Equation...

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