Showing papers on "Elliptic coordinate system published in 1982"
TL;DR: A comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given in this article, along with a general mathematical framework and error analysis common to such coordinate systems.
542 citations
TL;DR: In this paper, various types of generating systems for boundary-conforming coordinate systems based on the numerical solution of systems of elliptic partial differential equations are discussed, with particular emphasis on the determination of functions in these equations which control the distribution of the curvilinear coordinate lines in the field.
43 citations
TL;DR: In this article, an analysis of the local truncation error in the approximation of first and second order derivatives on a curvilinear grid is presented, and a number of examples are given to illustrate the two fundamental sources of truncation errors in the numerical solution of partial differential equations on such coordinate systems.
40 citations
TL;DR: The basic ideas of the construction and use of numerically-generated boundary-fitted coordinate systems for the numerical solution of partial differential equations are discussed in this paper, where all computation can be done on a fixed square grid in the rectangular transformed region regardless of the shape or movement of the physical boundaries.
36 citations
TL;DR: In this article, a family of mass-scaled coordinate systems is presented for the triatom i75n which the kinetic energy operator for large-amplitude vibrational motion is diagonal (unlike that in current local mode theories).
19 citations
TL;DR: In this paper, it was shown that Dirac's lightcone coordinate system provides an effective method for treating the geometry of Lorentz transformation in a rectangular coordinate system, and transformation properties of the coordinate variables and those of the derivatives are discussed in detail.
Abstract: It is shown that Dirac’s light‐cone coordinate system provides an effective method for treating the geometry of Lorentz transformation in a rectangular coordinate system. Transformation properties of the coordinate variables and those of the derivatives are discussed in detail. The Lorentz boost along a given direction is shown to be a coordinate transformation in which ’’cross products’’ are preserved. It is pointed out that the Lorentz boost is a symplectic transformation.
18 citations
11 citations
TL;DR: In this paper, a three-dimensional elliptic solver is used to generate surface-fitted coordinates about wing/wing-tip configurations, which are then used to compute interior coordinate control functions.
10 citations
01 Apr 1982
TL;DR: In this article, the basic ideas of the construction and use of numerically-generated boundary-fitted coordinate systems for the numerical solution of partial computation can be done on a fixed square grid in the rectangular transformed region regardless of the shape of movement of the physical boundaries.
Abstract: : The basic ideas of the construction and use of numerically-generated boundary-fitted coordinate systems for the numerical solution of partial computation can be done on a fixed square grid in the rectangular transformed region regardless of the shape of movement of the physical boundaries. A number of different types of configurations for the transformed region and the basic transformation relations from a cartesian system to a general curvilinear system are given. The material of this paper is applicable to all types of coordinate system generation.
9 citations
TL;DR: An analytical-numerical procedure for obtaining stress intensity factor solutions for an arbitrarily oriented crack in a long, thin circular cylindrical shell is presented in this paper, which involves obtaining a series solution to the governing shell equation in terms of Mathieu and modified Mathieu functions by the method of separation of variables and satisfying the crack surface boundary conditions numerically using collocation.
Abstract: An analytical-numerical procedure for obtaining stress intensity factor solutions for an arbitrarily oriented crack in a long, thin circular cylindrical shell is presented. The method of analysis involves obtaining a series solution to the governing shell equation in terms of Mathieu and modified Mathieu functions by the method of separation of variables and satisfying the crack surface boundary conditions numerically using collocation. The solution is then transformed from elliptic coordinates to polar coordinates with crack tip as the origin through a Taylor series expansion and membrane and bending stress intensity factors are computed. Numerical results are presented and discussed for the pressure loading case.
7 citations
TL;DR: In this article, the basic properties of the set Σ of parallel-surfaces coordinate (p.s.c.) system were studied for the most appropriate formulation of the differential form of the balance equations in fluid dynamic problems.
Abstract: The paper is devoted to the study of the basic properties of the setΣ of parallel-surfaces coordinate (p.s.c.) system previously introduced by the author for the most appropriate formulation of the differential form of the balance equations in fluid dynamic problems, where a «direction field» plays a fundamental role. This field is usually defined by the unit normal to a given surface S either known or unknown a-priori.
TL;DR: In this article, a coordinate-free characterisation of one coordinate for the Hamilton-Jacobi equation on a pseudo-Riemannian manifold was given in terms of an involutive family of Killing tensors.
Abstract: The authors extend an idea due to Woodhouse (1975) to give a coordinate-free characterisation of the orthogonal separation of one coordinate for the Hamilton-Jacobi equation on a pseudo-Riemannian manifold, in terms of an involutive family of Killing tensors. The coordinates can be computed from the Killing tensors.
Patent•
10 Jul 1982
TL;DR: In this article, the rotary matrix is any among 0, 1, -1 when a local coordinate axis and the entire coordinate axis coincide, and the coordinate value in the whole coordinate is then calculated by substitution calculations.
Abstract: PURPOSE:To reduce the time for calculation of coordinate values with simple constitution by corresponding beforehand rotation numbers and storing the local coordinate system that defines a shape when said system is not inclined with respect to the entire coordinate system. CONSTITUTION:The element of a rotary matrix is any among 0, 1, -1 when a local coordinate axis and the entire coordinate axis coincide. Rotation numbers are provided in correspondence to 24 kinds of the rotary matrix when the local coordinate system is not inclined with respect to the entire coordinate system. Values of x1, y1, z1 are inputted to the register RG-EX of the local coordinate axis and the signals of 1-24 and 25 are generated from a rotation number device RN. A switch SW is changed over so as to pass the output through a code inverter INV when a storage/generation device RVN which emits a control signal in correspondence to the numbers 1-24 outputs -1. Input is made to the register RG-GN of the entire coordinate system through a matrix calculation circuit MTP in the case of the number 25. The coordinate value in the entire coordinate is then calculated by substitution calculations.
TL;DR: In this paper, the authors used the technique of the boundary-fitted coordinate system to calculate the detailed velocity and temperature distributions of the flow over circular tubes, where all the physical boundaries are transformed into constant coordinate lines in the transformed coordinates.
TL;DR: In this article, the streaming term of the one-speed transport equation is expressed as a duality operation of modern tensor analysis, which allows one to write the equation easily in any orthogonal coordinate system.
Abstract: In this paper the streaming term of the one-speed transport equation is expressed as a duality operation of modern tensor analysis. This representation allows one to write the equation easily in any orthogonal coordinate system. An application of the present transformation technique is made to three different geometries of current interest in controlled thermonuclear reactor design, namely cylindrical and toroidal (with both circular and general elliptic cross sections).