A note on the mathematical formulation of the problem of numerical coordinate generation
Author:
Z. U. A. Warsi
Journal:
Quart. Appl. Math. 41 (1983), 221-236
MSC:
Primary 65N50; Secondary 53B20, 65D10
DOI:
https://doi.org/10.1090/qam/719506
MathSciNet review:
719506
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Abstract: A set of second order partial differential equations for the generation of three-dimensional grids around and between arbitrary shaped bodies has been proposed. These equations basically depend on the Gauss equations for a surface and have been structured in such a way that an automatic connection is established between the succeeding generated surfaces.
- Alan M. Winslow, Numerical solution of the quasilinear Poisson equation in a nonuniform triangle mesh, J. Comput. Phys. 1 (1967), 149–172. MR 241008, DOI https://doi.org/10.1016/0021-9991%2866%2990001-5
J. F. Thompson, F. C. Thames, and C. W. Mastin, Automatic numerical generation of body-fitted curvilinear coordinate system for field containing any number of arbitrary two-dimensional bodies, J. Comp. Phys. 15, 299–319 (1974)
- Joe F. Thompson, Zahir U. A. Warsi, and C. Wayne Mastin, Boundary-fitted coordinate systems for numerical solution of partial differential equations—a review, J. Comput. Phys. 47 (1982), no. 1, 1–108. MR 673712, DOI https://doi.org/10.1016/0021-9991%2882%2990066-3
Z. U. A. Warsi, A method for the generation of general three-dimensional coordinates between bodies of arbitrary shapes, Engineering and Industrial Research Station, Mississippi State University, Rept. MSSU-EIRS-80-7 (1980)
expm, Tensors and differential geometry applied to analytic and numerical coordinate generation, Engineering and Industrial Research Station, Mississippi State University, Rept. MSSU-EIRS-81-1 (1981)
- Z. U. A. Warsi, Basic differential model for coordinate generation, Appl. Math. Comput. 10/11 (1982), 41–77. Numerical grid generation (Nashville, Tenn., 1982). MR 675781, DOI https://doi.org/10.1016/0096-3003%2882%2990187-4
Z. U. A. Warsi and J. P. Ziebarth, Numerical generation of three-dimensional coordinates between bodies of arbitrary shapes, Ibid. pp. 717–728
- Luthur Pfahler Eisenhart, An Introduction to Differential Geometry, Princeton Mathematical Series, vol. 3, Princeton University Press, Princeton, N. J., 1940. MR 0003048
- Z. U. A. Warsi and J. F. Thompson, A noniterative method for the generation of orthogonal coordinates in doubly-connected regions, Math. Comp. 38 (1982), no. 158, 501–516. MR 645666, DOI https://doi.org/10.1090/S0025-5718-1982-0645666-3
- J. J. Stoker, Differential geometry, Pure and Applied Mathematics, Vol. XX, Interscience Publishers John Wiley & Sons, New York-London-Sydney, 1969. MR 0240727
- Erwin Kreyszig, Differential geometry, Mathematical Expositions, No. 11, University of Toronto Press, Toronto, 1959. MR 0108795
A. M. Winslow, Numerical solution of the quasi-linear Poisson equation in a non-uniform triangular mesh, J. Comp. Phys. 2, 149–172 (1967)
J. F. Thompson, F. C. Thames, and C. W. Mastin, Automatic numerical generation of body-fitted curvilinear coordinate system for field containing any number of arbitrary two-dimensional bodies, J. Comp. Phys. 15, 299–319 (1974)
J. F. Thompson, Z. U. A. Warsi, and C. W. Mastin, Boundary-fitted coordinate systems for numerical solution of partial differential equations—a review, J. Comp. Phys. 47, 1–108 (1982)
Z. U. A. Warsi, A method for the generation of general three-dimensional coordinates between bodies of arbitrary shapes, Engineering and Industrial Research Station, Mississippi State University, Rept. MSSU-EIRS-80-7 (1980)
expm, Tensors and differential geometry applied to analytic and numerical coordinate generation, Engineering and Industrial Research Station, Mississippi State University, Rept. MSSU-EIRS-81-1 (1981)
expm, Basic differential models for coordinate generation, Symposium on the Numerical Generation of Curvilinear Coordinate Systems and Use in the Numerical Solution of Partial Differential Equations, organized by Mississippi State University, sponsored by NASA and AFOSR. Radisson Plaza, Nashville, Tennessee, April 13–16 (1982); Appl. Math. Comp. 10, 41–77 (1982)
Z. U. A. Warsi and J. P. Ziebarth, Numerical generation of three-dimensional coordinates between bodies of arbitrary shapes, Ibid. pp. 717–728
L. P. Eisenhart, An introduction to differential geometry with use of the tensor calculus, Princeton University Press, Princeton, N.J., 1947
Z. U. A. Warsi and J. F. Thompson, A noniterative method for the generation of orthogonal coordinates in doubly-connected regions, Math. Comp. 38, 501–516 (1982)
J. J. Stoker, Differential geometry, Wiley-Interscience, New York, 1969
E. Kreyszig, Differential geometry, University of Toronto Press, Toronto, 1959
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Article copyright:
© Copyright 1983
American Mathematical Society
