Abstract
A new adaptive grid generation procedure is proposed, which combines a previously developed method that used Anderson's adaptive grid scheme along with a method for controlling grid spacing and orthogonality on all of the boundaries. The proposed method assigns the desired grid stretching over the smooth region during initial grid system generation and before grid adaptation is performed. After properly interpreting the smoothing term of the weighting function, the desired grid stretching is added to the adaptive grid scheme. Several test cases illustrate the method's feasibility.
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References
Anderson, D. A., Tannehill, J. C., and Pletcher, R. H. (1984).Computational Fluid Mechanics and Heat Transfer, Hemisphere, New York, Chap. 10, pp. 519–546.
Anderson, D. A., and Steinbrenner, J. (1986). Generating adaptive grids with a conventional grid scheme, AIAA Paper No. 86-0427.
Anderson, D. A. (1987a). Equidistribution schemes, Poisson generators, and adaptive grids,Appl. Math. Comput. 24, 211–227.
Anderson, D. A. (1987b). Adaptive grid scheme controlling cell area/volume, AIAA Paper No. 87-0202.
Dwyer, H. A., Kee, R. J., and Sanders, B. R. (1980). Adaptive grid method for problems in fluid mechanics and heat transfer,AIAA J. 18(10), 1205–1212.
Dwyer, H. A. (1984). Grid adaptive for problems in fluid dynamics,AIAA J. 22(12), 1705–1712.
Eiseman, P. R. (1987). Adaptive grid generation,Comput. Methods Appl. Meck Eng. 64, 321–376.
Hawken, D. F., Gottlieb, J. J., and Hansen, J. S. (1991) Review of some adaptive node-movement techniques in finite-element and finite-difference solutions of partial differential equations,J. Comput. Phys. 95, 254–302.
Hsu, K., and Lee, S. L. (1991). A numerical technique for two-dimensional grid generation with grid control at all of the boundaries,J. Comput. Phys. 92, 451–469.
Jeng, Y. N., and Liou, S. C. (1989). Modified multiple one-dimensional adaptive grid method,Numer. Heat Transfer B 15, 241–247.
Jeng, Y. N., and Chen, J. L. (1992). On the geometric conservation law of the finite-volume method for the SIMPLER algorithm and a proposed second order upwind scheme, to appear inNumer. Heat Transfer B: Fundamental.
Jeng, Y. N., and Liou, Y. C. (1992a). Adaptive grid generation by elliptic equations with grid control at all of the boundaries, revised byNumer. Heat Transfer B: Fundamental.
Jeng, Y. N., and Liou, Y. C. (1992b). Two modified versions of Hsu-Lee's elliptic solver of grid generation, to appear inNumer. Heat Transfer B: Fundamental.
Jeng, Y. N., Wu, T. J., and Panye, U. J. (1990). A class of high-resolution TVD schemes,The 4th National Conference on Theoretical and Applied Mechanics, Chung Li, Taiwan, R.O.C., STAMROC-14-L40.
Luong, P. V., Thompson, J. F., and Gatlin, B. (1991). Adaptive EAGLE: Solution-adaptive and quality-enhancing multiblock grids for arbitrary domains, AIAA paper No. 91-1953-cp.
Nielson, P., and Skovgard, O. (1988). A depth-adaptive grid using a control-function approach, inNumerical Grid Generation in Computational Fluid Mechanics, Sengupta, S.,et al. (eds.), Pineridge Press.
Shyy, W. (1986). An adaptive grid method for Navier-Stokes flow computation II: Grid addition,Appl. Numer. Math. 2, 9–19.
Shyy, W. (1987). An adaptive grid method for Navier-Stokes flow computation,Appl. Math. Comput. 21, 201–209.
Sorenson, R. L. (1986). Three-dimensional elliptic grid generation about fighter aircraft for zonal finite-difference computations, AIAA paper No. 86-0429.
Sorenson, R. L. (1980). A computer program to generate two-dimensional grid about airfoil and other shapes by the use of Poisson's equation, NASA TM-81198.
Steger, J. L., and Sorenson, R. L. (1979). Automatic mesh-point clustering near a boundary in grid generation with elliptic partial differential equations,J. Comput. Phys. 33, 405–510.
Thomas, P. D., and Middlecoff, J. F. (1980). Direct control of the grid point distribution in meshes generated by elliptic equations,AIAA J. 18(6), 652–656.
Thompson, J. F. (1984). Grid generation techniques in computational fluid dynamics,AIAA J. 22(11), 1505–1523.
Thompson, J. F. (1985). A survey of dynamically adaptive grids in the numerical solution of partial differential equations,Appl. Numer. Math. 1, 3–28.
Thompson, J. F., Thames, F. C., and Mastin, C. W. (1974). Automatic numerical generation of body-fitted curvilinear coordinate systems for fields containing any number of arbitrary two-dimensional bodies,J. Comput. Phys. 15, 299–312.
Thompson, J. F., Thames, F. C., and Mastin, C. W. (1977). TOMCAT—A code for numerical generation of boundary-fitted curvilinear coordinate systems on fields containing any number of arbitrary two-dimensional bodies,J. Comput. Phys. 24, 274–302.
Thompson, J. F., Warsi, Z. U. A., and Mastin, C. W., (1982). Boundary-fitted coordinate systems for numerical solution of partial differential equations—A review,J. Comput. Phys. 47, 1–108.
Visbal, M., and Knight, D. (1982). Generation of orthogonal and nearly orthogonal coordinates with grid control near boundaries,AIAA J. 20(3), 305–306.
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Jeng, Y.N., Liou, Y.C. A new adaptive grid generation by elliptic equations with orthogonality at all of the boundaries. J Sci Comput 7, 63–80 (1992). https://doi.org/10.1007/BF01060211
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DOI: https://doi.org/10.1007/BF01060211