# l16 - Lecture 16 Diffusion on Unstructured Meshes(Contd 1...

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1 Lecture 16: Diffusion on Unstructured Meshes (Cont’d)

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2 Last Time … Last time, we: Saw that we need to find gradients for secondary flux calculation (and for other reasons) Saw that finding gradients is relatively simple on structured meshes Used gradient theorem approach to find cell-centroid gradient on unstructured mesh
3 This Time… We will Look at another way to find gradients on unstructured meshes » Least squares method Discussion of the effect of secondary gradient calculation on coefficient structure and convergence Implementation issues

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4 Least Squares Method for Gradient Calculation Estimate values at neighboring cell-centroids assuming local linearity and using cell gradient at C0 Figure out an “error” in the estimate Find gradient components at C0 to minimize error
5 Least Squares Method (Cont’d) Let’s assume that local variation is linear We can estimate value at C1 centroid as:

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6 Least Squares Method (Cont’d) Can do similar manipulation at all face centroids j=1,2,…,J: Can write a set of equations where M is Jx2 matrix
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l16 - Lecture 16 Diffusion on Unstructured Meshes(Contd 1...

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