l12 - Lecture 12 Stability Analysis Diffusion on...

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1 Lecture 12: Stability Analysis Diffusion on Unstructured Meshes
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2 Last Time… Completed unsteady scheme discussion » Crank Nicholson scheme and its properties Truncation error analysis » Mean value approximations are second-order accurate » Implicit scheme is first-order accurate
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3 This Time… Von Neumann stability analysis » Apply to explicit scheme and establish stability limits Diffusion on orthogonal unstructured meshes » What changes with respect to Cartesian?
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4 Von Neumann Stability Analysis For steady problems: » Can we obtain a solution using an iterative scheme? For unsteady problems » Will the numerical solution be bounded in time if the original problem yields a bounded solution in time? Note analogy between iteration and time-stepping!
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5 Stability of Explicit Scheme Explicit scheme in 1D:
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6 Error Definition Consider “exact solution” of the discrete equation, . » This is the solution to infinite precision Numerical solution to machine precision is Error: Substitute into discrete equation: But satisfies discrete equation exactly.
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7 Error Equation Therefore error satisfies: Now expand error in Fourier series
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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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l12 - Lecture 12 Stability Analysis Diffusion on...

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