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Boundary-fitted curvilinear coordinate systems for solution of partial differential equations on fields containing any number of arbitrary two-dimensional bodies
TLDR
In this article, a method is presented for automatic numerical generation of a general curvilinear coordinate system with coordinate lines coincident with all boundaries in a general multi-connected two-dimensional region containing any number of arbitrarily shaped bodies.Abstract:
A method is presented for automatic numerical generation of a general curvilinear coordinate system with coordinate lines coincident with all boundaries of a general multi-connected two-dimensional region containing any number of arbitrarily shaped bodies. No restrictions are placed on the shape of the boundaries, which may even be time-dependent, and the approach is not restricted in principle to two dimensions. With this procedure the numerical solution of a partial differential system may be done on a fixed rectangular field with a square mesh with no interpolation required regardless of the shape of the physical boundaries, regardless of the spacing of the curvilinear coordinate lines in the physical field, and regardless of the movement of the coordinate system in the physical plane. A number of examples of coordinate systems and application thereof to the solution of partial differential equations are given. The FORTRAN computer program and instructions for use are included.read more
Citations
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Spectral methods for problems in complex geometries
TL;DR: In this paper, a new iteration procedure is introduced to solve the full matrix equations resulting from spectral approximations to nonconstant coefficient boundary-value problems in complex geometries, and the work required to solve these spectral equations exceeds that of solving the lowest-order finite-difference approximation to the same problem by only O(N log N).
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Boundary-fitted coordinate systems for numerical solution of partial differential equations—A review
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.
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Direct Control of the Grid Point Distribution in Meshes Generated by Elliptic Equations
P. D. Thomas,J. F. Middlecoff +1 more
TL;DR: In this article, an effective method of interior grid control is presented based on a modified elliptic system containing free parameters for a simply connected region, the free parameters are computed from the Dirichlet boundary values.
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TOMCAT - A code for numerical generation of boundary-fitted curvilinear coordinate systems on fields containing any number of arbitrary two-dimensional bodies
TL;DR: In this article, a method for automatic generation of boundary-fitted curvilinear coordinate systems, where the transformed coordinates are solutions of an elliptic differential system in the physical plane and where the coordinate lines are coincident with all boundaries of a general multiply-connected, two-dimensional region containing any number of arbitrarily shaped bodies, is described along with a suitable computer code for implementing the method.
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A compressible three‐dimensional design method for radial and mixed flow turbomachinery blades
TL;DR: In this paper, a fully three-dimensional compressible inverse design method for the design of radial and mixed flow turbomachines is described, where the distribution of the circumferentially averaged swirl velocity rV-theta-BAR on the meridional geometry of the impeller is prescribed and the corresponding blade shape is computed iteratively.
References
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TL;DR: In this paper, the principles of ideal-fluid aerodynamics were proposed. And they were applied to aerodynamic principles in the field of aerodynamics, including the principle of ideal fluid dynamics.
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A simple scheme for generating general curvilinear grids
A.A. Amsden,C.W Hirt +1 more
TL;DR: In this article, an intuitively simple approach is presented for the computer generation of two-dimensional curvilinear grids suitable for finite difference solutions of problems in the field of continuum dynamics.
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Development of a general finite difference approximation for a general domain part I: Machine transformation
TL;DR: In this paper, an equilateral triangle mesh plane is employed for a general, second-order quasi-linear elliptic partial differential equation subject to a general third boundary value condition in a general domain.