The direct matrix imbedding technique for computing three-dimensional potential flow about arbitrarily shaped bodies

The direct matrix imbedding technique is used to solve Laplace's equation for the velocity potential numerically about arbitrarily shaped bodies with normal gradient boundary conditions in two and three dimensions. The bodies are imbedded in Cartesian grids overlaying relatively large rectangular and box regions. Solutions are obtained only in those parts of the grid necessary for constructing solutions to potential flow problems. An important subclass of these problems, considered in this paper, is ship wave problems in channels. Uniform and stretched Cartesian grids are considered, and solutions are obtained very quickly. Results are presented.