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Manuscript Title: Orthogonalization of discrete coordinates.
Authors: C.W. Davies
Program title: RECT
Catalogue identifier: AAQW_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 23(1981)427
Programming language: Fortran.
Computer: CDC 7600.
Operating system: SCOPE 2.1.5.
RAM: 13K words
Word size: 60
Keywords: General purpose, Plasma physics, Other numerical, Orthogonalization, Discrete orthogonal Coordinates, Boundary fitted, Waterbag methods, Stability.
Classification: 4.12, 19.6.

Nature of problem:
A two-dimensional boundary fitted orthogonal coordinate mesh may be required initially in an Eulerian calculation or at each time step in a semi-Lagrangian or waterbag code. A procedure for orthogonalizing a non-orthogonal coordinate mesh is described which preserves one set of coordinates. The preserved coordinate lines may be open or closed.

Solution method:
The procedure is based upon an initial-value formulation with the non- orthogonal coordinates as the independent variable. The initial-value problem is solved in its partial differential equation form.

Restrictions:
The initial non-orthogonal mesh must be smooth.

Running time:
The running time scales linearly with the number of mesh points. On a CDC 7600 RECTC requires 0.037 s per 1000 points and RECTO requires 0.016 s per 1000 points.