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Elliptic coordinate system

About: Elliptic coordinate system is a research topic. Over the lifetime, 670 publications have been published within this topic receiving 11135 citations. The topic is also known as: elliptical coordinate system & elliptic coordinates.


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Journal ArticleDOI
TL;DR: In this article, explicit expressions of the full Hamiltonian of a tri-atomic system in the hyperspherical elliptic (HSE) coordinates are derived from the expressions in the Delves coordinates and a numerical algorithm is presented to evaluate the surface eigenfunctions including all the effects of Coriolis coupling terms.
Abstract: Explicit expressions of the full Hamiltonian of tri-atomic system in the hyperspherical elliptic (HSE) coordinates are derived. The derivation is made from the expressions in the Delves coordinates. A numerical algorithm is also presented to evaluate the surface eigenfunctions including all the effects of Coriolis coupling terms. The whole formalism is numerically tested by using the Cl + DH and O( 1 D) + HCl reaction systems. The HSE coordinate system, which is well-known to be powerful to elucidate reaction mechanisms especially for heavy-light-heavy systems, is now ready to be applied for clarifying full quantum dynamics of such systems.

3 citations

Journal ArticleDOI
TL;DR: New isochoric finite deformations may be generated from any such deformation described in rectangular Cartesian coordinates by changing coordinate systems as mentioned in this paper. But this is not the case for all deformations.
Abstract: New isochoric finite deformations may be generated from any such deformation described in rectangular Cartesian coordinates by changing coordinate systems.

3 citations

01 Mar 1984
TL;DR: In this paper, it is accepted that body-fitted coordinate systems give a much better description of complex flow geometries than traditional rectangular grids and thus are more accurate in solving Navier-Stokes equations.
Abstract: An accurate numerical solution of the Navier-Stokes equations is strongly dependent on the description of the flow geometry. In the past, rectangular grids led to an ill description of curved boundaries and consequently hindered finite-difference solutions. Now, it is accepted that body-fitted coordinate systems give a much better description of complex flow geometries. The generation of body-fitted curvilinear coordinate grids in two dimensions by the solution of a nonlinear system of elliptic equations has been proposed Thompson. It has been extended to three dimensions and applied in practical configurations.

3 citations

Journal ArticleDOI
TL;DR: In this article, a two-dimensional natural convection around a heated finite flat plate oriented at an arbitrary angle, α, with respect to the gravity force is formulated in terms of an elliptic coordinate system, and the spectral series expansion is used to reduce the governing coupled partial differential equations to three sets of second-order ordinary differential equations.
Abstract: Steady two-dimensional natural convection around a heated finite flat plate oriented at an arbitrary angle, α, with respect to the gravity force is formulated in terms of an elliptic coordinate system. The method of spectral series expansion is used to reduce the governing coupled partial differential equations to three sets of second-order ordinary differential equations. These equations are truncated and then numerically integrated by the finite-element method of collocation. The effect of boundary conditions on the outer boundary of the computational field is discussed. The flows for Ra = 1000.0, Pr = 0.7 and α = 0,2, 45, and 90 degrees are analyzed using illustrations of fluid flow patterns, graphs of surface vorticity and local Nusselt number, and contour plots of isotherms.

3 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20237
202211
202111
202010
201913
201810