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Potential flow past a perturbed circle: an example of domain perturbation

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Potential flow past a perturbed circle: an example of domain perturbation. The problem of potential flow past a circular object is a well-studied problem in fluid mechanics governed by the Laplace equation. We wish to study the flow around a circle which is slightly perturbed. The boundary is now described as r = R(1 + cos θ) The solution for the streamfunction for the base problem where the boundary is at r = R is that for a circle studied in Section 15.4.2. Now set up the domain perturbation analysis for this problem with the above perturbed boundary and solve for the modified domain.