An Alternative Complex Boundary Element Method for Nonlinear Free Surface Problems
MICHIGAN UNIV ANN ARBOR
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A complex variable boundary element method is developed for potential flow problems by applying Cauchys integral theorem to the complex velocity. The resulting integral equation is a function of the normal and tangential velocity components on the boundary. A new form of the full nonlinear dynamic free surface boundary condition is used to describe the evolution of tangential velocities. This alternate method solves for flows with field singularities more easily than the conventional method, which uses the complex velocity potential. Also, the velocity field is given directly without the need for numerical differentiation. Under the new formulation, the dynamic free surface boundary condition does, however, become more complicated. As a result, while the new form of the boundary element method has definite advantages for fixed boundaries, its usefulness for free surface problems is mixed.
- Theoretical Mathematics
- Fluid Mechanics