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Numerical studies on non-linear free surface flow using generalized Schwarz–Christoffel transformation by J. M. Chuang is a Engineering article available to read on EtoBox.

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This paper deals with a technique to transform a free surface flow problem in the physical domain with an unknown boundary to a standard domain that has a fixed boundary. All the difficulties in the physical domain are reduced to finding an unknown mapping function that can be solved iteratively in a standard domain. A derivation is first presented to express an analytic function in terms of the boundary value of its imaginary part. Using a relationship between boundaries of the standard and the physical domains, a formula for the generalized Schwarz-Christoffel transformation is then developed. Based on the generalized Schwarz-Christoffel integral and the Hilbert transform, a pair of non-linear boundary integro-differential equations in an infinite strip is formulated for solving fully non-linear free surface flow problems. The boundary integral equations are then discretized with quadratic elements in an untruncated standard domain and solved by the Levenberg -Marquardt algorithm. Several examples of supercritical flow past obstructions are provided to demonstrate the flexibility and the accuracy of the proposed numerical scheme.

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Author

J. M. Chuang

Publisher

John Wiley and Sons; Wiley (John Wiley & Sons); John Wiley & Sons Inc.; Wiley (ISSN 0271-2091)

Published

2000

Language

EN

Field

Engineering (Physical Sciences)