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- W2023108522 abstract "PARTI of this series (1) described how the relaxation method could be extended from two to three dimensions in order to solve boundary value potential problems. In this paper considerably more advanced solutions of Laplace's equation are presented; they require the introduction into three-dimensional relaxation of graded lattices and of the determination of initially unknown boundaries or interfaces. The problems solved in illustration concern the potential flow of an incompressible fluid round three-dimensional aerofoils; two cases are solved in detail, one for the flow round a straight wing and one for the flow round a swept-back wing. Results are presented in the form of numerical values of the velocity-potential of the flow at the points of a relaxation lattice, together with certain derived curves which show the variation of the circulation and of the position of the aerodynamic centre along the span. The problem in three dimensions necessitates a formulation which would not normally be made for the corresponding problem in two dimensions; consequently the method is described firstly, for simplicity, in relation to such a two-dimensional problem. The existence in this case of an exact analytical solution makes possible a comparison with the relaxational results." @default.
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- W2023108522 date "1953-01-01" @default.
- W2023108522 modified "2023-10-16" @default.
- W2023108522 title "THE APPLICATION OF RELAXATION METHODS TO THE SOLUTION OF DIFFERENTIAL EQUATIONS IN THREE DIMENSIONS" @default.
- W2023108522 doi "https://doi.org/10.1093/qjmam/6.1.81" @default.
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