Thompson, Warsi, Mastin - Numerical Grid Generation, страница 44

A. and Mastin, C. W., "Boundary-Fitted Coordinate Systems for Numerical Solutionof Partial Differential Equations -- A Review", Journal of Computational Physics, 47, 1, 1982.2. Thompson, Joe F. (Ed.) Numerical Grid Generation, North-Holland 1982. (Also published as Vol. 10 11 of AppliedMathematics and Computation, 1982).3. Smith, Robert E., (Ed), Numerical Grid Generation Techniques, NASA Conference Publication 2166, NASALangley Research Center, 1980.4. Ghia, K. N. and Ghia, U., (Ed), Advances in Grid Generation, FED-Vol. 5, ASME Applied Mechanics,Bioengineering, and Fluids Engineering Conference, Houston, 1983.5. Thompson, Joe F., "Grid Generation Techniques in Computational Fluid Dynamics", AIAA Journal, 22, 1505, 1984.6. Halsey, Douglas, "Conformal Grid Generation for Multi-element Airfoils", Numerical Grid Generation, Ed. Joe F.Thompson, North-Holland, 585, 1982.7. Ives, David C., "Conformal Grid Generation", Numerical Grid Generation, Ed.

Joe F. Thompson, North-Holland,107, 1982.8. Smith, Robert E., "Three-Dimensional Algebraic Grid Generation", AIAA-83-1904, AIAA 6th Computational FluidDynamics Conference, Danvers, Massachusetts, 1983.9. Thompson, J. F. and Warsi, Z. U. A., "Three-Dimensional Grid Generation from Elliptic Systems", AIAA-83-1905,AIAA 6th Computational Fluid Dynamics Conference, Danvers, Massachussetts, 1983.10. Coleman, Roderick M., "Generation of Boundary-Fitted Coordinate Systems Using Segmented ComputationalRegions", Numerical Grid Generation, Ed. Joe F.

Thompson, North-Holland, 633, 1982.11. Rubbert, P. E. and Lee, K. D., "Patched Coordinate Systems", Numerical Grid Generation, Ed. Joe F. Thompson,North-Holland, 235, 1982.12. Thomas, P. D., "Numerical Generation of Composite Three-Dimensional by Quasilinear Elliptic Systems",Numerical Grid Generation, Ed. Joe F. Thompson, North-Holland, 667, 1982.13. Miki, Kazuyoshi and Takagi, Toshiyuki, "A Domain Decomposition and Overlapping Method for the Generation ofThree-Dimensional Boundary-Fitted Coordinate Systems", Journal of Computational Physics, 53, 319, 1984.14. Thompson, Joe F., unpublished research, 1984.15.

Warsi, Z. U. A., "Tensors and Differential Geometry Applied to Analytic and Numerical Coordinate Generation",MSUU-EIRS-81-1, Mississippi State University, 1981.16. Eiseman, P. R., "Geometric Methods in Computational Fluid Dynamics", ICASE 80-11, NASA Langley ResearchCenter, 1980.17. Thompson, Joe F. and Mastin, C. Wayne, "Order of Difference Expressions on Curvilinear Coordinate Systems",Advances in Grid Generation, FED-Vol.

5, Ed. K. N. Ghia and U. Ghia, ASME Applied Mechanics, Bioengineering,and Fluids Engineering Conference, Houston, 1983.18. Vinokur, Marcel, "On One-Dimensional Stretching Functions for Finite-Difference Calculations", Journal ofComputational Physics, 50, 215, 1983.19. Warsi, Z. U. A., "Basic Differential Models for Coordinate Generation", Numerical Grid Generation, Ed. Joe F.Thompson, North-Holland, 41, 1982.20.

Mastin, C. Wayne and Thompson, Joe F., "Elliptic Systems and Numerical Transformations", Journal ofMathematical Analysis and Applications, 62, 52, 1978.21. Mastin, C. Wayne and Thompson, Joe F., "Transformationof Three-Dimensional Regions onto RectangularRegions by Elliptic Systems", Numerische Mathematik, 29, 397, 1978.22. Mastin, C. Wayne and Thompson, Joe F., "Discrete Quasiconformal Mappings", Journal of Applied Mathematicsand Physics (ZAMP), 29, 1978.23. Mastin, C. W.

and Thompson, J. F., "Quasiconformal Mappings and Grid Generation", SIAM Journal On Scientificand Statistical Computing, 5, 305, 1984.24. Sorenson, R. L., "A Computer Program to Generate Two-Dimensional Grids About Airfoils and Other Shapes bythe Use of Poisson's Equations", NASA Ames Research Center, NASA TM 81198, 1980.25.

Sorenson, Reese L., "Grid Generation by Elliptic Partial Differential Equations for a Tri-Element Augmentor-WingAirfoil", Numerical Grid Generation, Ed. Joe F. Thompson, North-Holland, 653, 1982.26. Sorenson, R. L. and Steger, J. L., "Grid Generation in Three Dimensions by Poisson Equations with Control of CellSize and Skewness at Boundary Surfaces", Advances in Grid Generation, FED-Vol. 5, Ed. K. N. Ghia and U. Ghia,ASME Applied Mechanics, Bioengineering, and Fluids Engineering Conference, Houston, 1983.27. Warsi, Z. U.

A., "A Note on the Mathematical Formulation of the Problem of Numerical Coordinate Generation",Quarterly of Applied Mathematics, 41, 221, 1983.28. Steger, J. L. and Chaussee, D. S., "Generation of Body Fitted Coordinates Using Hyperbolic Partial DifferentialEquations", SIAM J. Sci. Stat. Comput. 1, 431, 1980.29.

Steger, J. L. and Sorenson, R. L., "Use of Hyperbolic Partial Differential Equations to Generate Body FittedCoordinates", Numerical Grid Generation Techniques, Ed. Robert E. Smith, NASA-CP-2166, 463, 1980.30. Nakamura, S., "Marching Grid Generation Using Parabolic Partial Differential Equations", Numerical GridGeneration, Ed. Joe F. Thompson, North-Holland, 775, 1982.31. Smith, Robert E., "Algebraic Grid Generation", Numerical Grid Generation, Ed.

Joe F. Thompson, North Holland,137, 1982.32. Eiseman, P. R., "A Multi-Surface Method of Coordinate Generation", Journal of Computational Physics, 33, 118,1979.33. Eiseman, Peter R. and Smith, Robert, "Mesh Generation Using Algebraic Techniques", Numerical Grid GenerationTechnigues, Ed. Robert E. Smith, NASA CP-2166, 1980.34. Eiseman, Peter R., "Automatic Algebraic Coordinate Generation", Numerical Grid Generation, Ed.

Joe F.Thompson, North-Holland, 447, 1982.35. Eiseman, Peter R., "Coordinate Generation with Precise Controls Over Mesh Properties", Journal of ComputationalPhysics, 47, 331, 1982.36. Eiseman, Peter R., "High Level Continuity for Coordinate Generation with Precise Controls", Journal ofComputational Physics, 47, 352, 1982.37.

Eiseman, Peter R. "Grid Generation for Fluid Mechanics Computations", Annual Review of Fluid Mechanics, Vol.17, 1985.38. Eiseman, Peter R. unpublished result referred to in Ref. [33].39. Roberts, A., "Automatic Topology Generation and Generalized B-Spline Mapping", Numerical Grid Generation,Ed. Joe F. Thompson, North-Holland, 465, 1982.40. Gordon, William J. and Thiel, Linda C., "Transfinite Mappings and Their Application to Grid Generation",Numerical Grid Generation, Ed. Joe F. Thompson, North-Holland, 171, 1982.41. Gordon, W. J.

"Blending Function Methods of Bivariate and Multivariate Interpolation", SIAM J. of NumericalAnalysis, 8, 158, 1971.42. Eiseman, Peter R., "Orthogonal Grid Generation", Numerical Grid Generation, Ed. Joe F. Thompson, NorthHolland, 193, 1982.43. Ives, D. C. and Siddons, W. D., "Orthogonal Grid Generation", AIAA-84-1248, AIAA/SAE/ASME 20th JointPropulsion Conference, Cincinnati, 1984.44. Kober, H., Dictionary of Conformal Representations, Dover, New York, 1952.45. Thompson, Joe F., "A Survey of Dynamically-Adaptive Grids in the Numerical Solution of Partial DifferentialEquations", to appear in Journal of Numerical Mathematics, 1984.

(also AIAA-84-1606, AIAA Fluid and PlasmaDynamics Conference, Snowmass, Colorado, 1984).46. Dwyer, H. A., Smooke, Mitchell, D. and Kee, Robert J., "Adaptive Gridding for Finite Difference Solutions to Heatand Mass Transfer Problems", Numerical Grid Generation, Ed. Joe F. Thompson, North-Holland, 339, 1982.47. Brackbill, J. U. and Saltzman, J. S., "Adaptive Zoning for Singular Problems in Two Dimensions", Journal ofComputational Physics, 46, 342, 1982.48. Anderson, Dale, A., and Rai, M. M., "The Use of Solution Adaptive Grids in Solving Partial DifferentialEquations", Numerical Grid Generation, ed. Joe F.

Thompson, North-Holland, 317. 1982.49. Miller, Keith and Miller, Robert N., "Moving Finite Elements. I", SIAM Journal of Numerical Analysis, 18, 1019,1981.50. Miller, Keith, "Moving Finite Elements. II", SIAM Journal of Numerical Analysis, 18, 1033, 1981.51. Weatherill, N.

C. and Forsey, C. R. "Grid Generation and Flow Calculations for Complex Aircraft GeometriesUsing a Multi-Block Scheme", AIAA-84-1665, AIAA 17th Fluid Dynamics, Plasma Dynamics, and LasersConference, Snowmass, CO, 1984.52. Rai, N. M. "A Conservative Treatment of Zonal Boundaries for Euler Equations Calculations", AIAA-84-0164,AIAA 22nd Aerospace Sciences Meeting, Reno, NV, 1984.53. Hessenius, K. A. and Rai, M. M., "Applications of a Conservative Zonal Scheme to Transient and GeometricallyComplex Problems", AIAA-S4-1532, AIAA 17th Fluid Dynamics, Plasma Dynamics, and Lasers Conference,Snowmass, CO, 1984.GRID ILLUSTRATION REFERENCESThe grids used for illustration are drawn from those in the works cited here:Page20 Anderson, 0. L., Davis, R. T., Hankins, G. B., and Ewards, D.

E., "Solution of Viscous Internal Flows onCurvilinear Grids Generated by the Schwarz-Christoffel Transformation." in Ref. [2].21 Kumar, D., Hester, L. R., and Thompson, J. F., "Development of Partial Channel Flow for Arbitrary Input VelocityDistribution Using Boundary-Fitted Coordinate Systems", in Nonsteady Fluid Dynamics, ASME Winter AnnualMeeting, San Francisco, 53, 1978.22, McWhorter, John C., "Solid Mechanics Applications of Boundary Fitted Coordinate Systems", in Ref. [2].2324, Lee, K. D., Huang, Yu, N.

J., and Rubbert, P. E., "Grid Generation for General Three-Dimensional Configurations",in Ref. [3].2527, Coleman, Roderick M., "Generation of Boundary-Fitted Coordinate Systems Using Segmented ComputationalRegions", in Ref. [2].2829 Thompson, J. F., Thames, F. C., and Mastin, C. W., "'TOMCAT' -- A Code for Numerical Generation of BoundaryFitted Curvilinear Coordinate Systems on Fields Containing any Number of Arbitrary Two-Dimensional Bodies",Journal of Comptational Physics, 245, 1977.30 Reddy, R.

N. and Thompson, Joe F., "Numerical Solution of Incompressible Navier-Stokes Equations in theIntegro-Differential Formulation Using Boundary-Fitted Coordinate Systems", Proceedings of the AIAA 3rdComputational Dynamics Conference, Albuquerque, 1977.33 Thompson, J. F., "A Boundary-Fitted Coordinate Code for General Two-Dimensional Regions with Obstacles andBoundary Intrusions", Technical Report E-83-8, U.S. Army Engineer Waterways Experiment Station, Vicksburg,Mississippi, 1983.34 Thompson, J. F., Thames, F. C., and Mastin, C.

W., "'TOMCAT' -- A code for Numerical Generation of BoundaryFitted Curvilinear Coordinate Systems on Fields Containing any Number of Arbitrary Two-Dimensional Bodies",Journal of Comptuational Physics, 245, 1977.35, Thompson, J. F., Thames, F. C., and Mastin, C. W., "'TOMCAT' -- A Code for Numerical Generation of BoundaryFitted Curvilinear Coordinate Systems on Fields Containing any Number of Arbitrary Two-Dimensional Bodies",Journal of Computational Physics, 245, 1977.3738 Halsey, Douglas, "Conformal Grid Generation for Multi-Element Airfoils", in Ref.

[2].39 Long, W. S., "Two-Body Coordinate System Generation Using Body-Fitted Coordinate System and ComplexVariable Transformation", M.S. thesis, Mississippi State University, 1977.40 Coleman, R. M. "NUMESH: A Computer Program to Generate Finite Difference Meshes for Arbitrary DoubleConnected Two-Dimensional Regions," CMLD-77-05, David W. Taylor Naval Ship Research and DevelopmentCenter, 1977.45 Haussling, Henry J., "Solution of Nonlinear Water Wave Problems Using Boundary-Fitted Coordinate Systems," inRef.