l15 - Lecture 15: Diffusion on Unstructured Meshes (contd)...

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1 Lecture 15: Diffusion on Unstructured Meshes (cont’d)
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2 Last Time We Figured out how to use a local coordinate system to complete our discretization Saw that the face fluxes result in primary and secondary gradients Saw that secondary gradients can destroy boundedness
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3 This Time We will Discuss how to address boundary conditions Start looking at how to compute gradients on unstructured meshes for use in the secondary gradient term
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4 Boundary Conditions Near-boundary cell balance: Boundary flux: Secondary gradient term:
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5 Boundary Conditions (Cont’d) Boundary flux : Discretize primary component: Write secondary gradient in terms (total-primary):
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6 Boundary Conditions (Cont’d) Secondary flux at boundary: Find boundary gradient from cell value Thus:
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7 Dirichlet Boundary Conditions For Dirichlet bc: Use given value in finding boundary flux: Use given value here Use given value to compute gradient
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Discrete Equation Scarborough
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l15 - Lecture 15: Diffusion on Unstructured Meshes (contd)...

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