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NUEN-430 Lecture 6

NUEN-430 Lecture 6 - NUEN 430 Lecture 6 Our purpose here is...

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NUEN 430 Lecture 6 Our purpose here is to derive a general geometry version of the cell-centered diffusion discretization with material inhomogeneities. Our first task is to derive an expression for an interior- mesh current with variable cell widths and cross-sections that are constant within each cell , but very between cells . Consider the two cells shown below where cell centers carry integer indices and cell edges carry half-integer indices. Let and denote the absorption cross-section, diffusion coefficient, and cell width, respectively, for cell i. We cannot take a difference across a cell interface if there is a discontinuity in the diffusion coefficient, because the normal component of the scalar flux gradient will be discontinuous across the interface. Thus we add a scalar flux unknown at the interface, take a difference to the left of the interface, take a difference to the right of the interface, and equate the associated normal components of the currents obtain first the interface scalar flux and then the interface current.
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