Showing papers on "Elliptic coordinate system published in 1978"
TL;DR: In this article, a grid-generation procedure is proposed based on the solution of Laplace's equation for the Cartesian coordinates of the orthogonal grid nodes, and the combined procedure is tested and demonstrated by calculating the flow properties in a diffuser of sufficient divergence to cause recirculation.
119 citations
TL;DR: In this paper, a coordinate system suitable for numerical computation of viscous transonic cascade flows is constructed, which consists of coordinate loops surrounding the airfoil and radial coordinate lines normal to the air-foil surface.
49 citations
01 Sep 1978
TL;DR: In this paper, the Dirichlet boundary conditions are used for the numerical solution of nonorthogonal boundary-fitted coordinate systems, i.e., a coordinate line coincides with the boundary.
Abstract: : A procedure for the numerical solution of nonorthogonal boundary-fitted coordinate systems, i.e., a coordinate line coincides with the boundary, is presented. This method generates curvilinear coordinates as the solution of two elliptic partial differential equations with Dirichlet boundary conditions, one coordinate being specified to be constant on each of the boundaries, and a distribution of the other specified along the boundaries. No restrictions are placed on the irregularity of the boundaries, which are even allowed to be time dependent, such as might occur in problems involving the computation of the location of the free surface, flooding boundaries, and streambank erosion problems. In addition, fields containing multiple bodies or branches can be handled as easily as simple geometries. Regardless of the shape and number of bodies and regardless of the spacing of the curvilinear coordinate lines, all numerical computations, both to generate the coordinate system and to subsequently solve the system of partial differential equations of interest, e.g., the vertically integrated hydrodynamic equations, are done on a rectangular grid with square mesh.
7 citations
01 Sep 1978
TL;DR: In this paper, a method for numerically generating boundary-fitted coordinate systems for three-dimensional regions containing ship-like bodies is presented, which involves a transformation which maps the region of interest in physical space onto a region in computational space where a uniform grid is defined.
Abstract: : A method for numerically generating boundary-fitted coordinate systems for three-dimensional regions containing ship-like bodies is the subject of this report. This procedure involves a transformation which maps the region of interest in physical space onto a region in computational space where a uniform grid is defined. The result is a curvilinear coordinate system in the physical region having coordinate lines coincident with all boundary contours.
1 citations