本研究主要是應用卡氏網格法(Cartesian Grid Method)與共位體心式有限體積法(Collocated Cell-Centered Finite Volume Method)來模擬高分子押出成型程序。一個自動化的卡氏網格產生程式已經完成，使用者只需輸入STL格式的幾何形狀與網格切割參數即可產生出卡氏網格。卡氏網格的層數越多，網格形狀越接近實際之幾何形狀。卡氏網格在幾何邊界所形成之鋸齒狀邊界對於模擬計算之收斂性有不良的影響，然而，在邊界平滑無鋸齒狀的情形下，卡氏網格層數越多，程式收斂情形越佳。本研究使用卡氏網格來模擬高分子在一個魚尾形平板押出模具中流動情形，求解其速度，壓力，溫度及黏度分佈，均得到合理之結果，證明卡氏網格法，一個快速且自動化的網格產生方式，在塑膠加工CAE分析方面確實有其應用價值。

This research applies Cartesian Grid Method along with Collocated Cell-Centered Finite Volume Method to simulate polymer extrusion process. A automated Cartesian Grid generation program is developed. Users only have to input STL format geometry and mesh parameters to generate Cartesian Grid. The outline of the grid gets closer to actual geometry as the level of Cartesian Grid grows. The saw-toothed geometric boundary of Cartesian Grid has bad influences to the simulation convergence. However, under the circumstances that grid is smooth (i.e. without the saw-tooth boundary), the simulation converges better as the grid level increases. This study uses Cartesian Grid to simulate polymer flow in a fishtail flat extrusion die, reasonable velocity, pressure, temperature and viscosity profile is obtained. This research proves that Cartesian Grid method, a fast and fully automated mesh generation method, has practical application in the CAE analysis of polymer processes.

1. E. A. Muccio, “Plastics Processing Technology”, ASM International, United States of America (1994).
2. D. H. Morton-Jones, “Polymer Processing”, Chapman & Hall, London (1989).
3. W. Michaeli, “Extrusion Dies for Plastics and Rubber”, Hanser Publishers, New York (1992).
4. C. Rauwendaal, “Polymer Extrusion”, Hanser Publishers, New York (1990).
5. J. H. Ferziger, M Peric, “Computational Methods for Fluid Dynamics”, Springer, New York (1996)
6. M. J. Aftosmis, “Solution Adaptive Cartesian Grid Methods for Aerodynamic Flows with Complex Geometries”, Lecture Notes for 28th Computational Fluid Dynamics Lecture Series, von Karman Institute for Fluid Dynamics (1997)
7. Reyhner, T. A., “Cartesian Mesh Solution for Axisymmetric Transonic Potential Flow Around Inlets,” AIAA Journal, vol. 15, No. 5, 1977, pp. 624-631.
8. Purvis, J., and Burkhalter, J., “Prediction of Critical Mach Number for Store Configurations,” AIAA Journal, vol. 17, No. 2, 1979.
9. Wedan, B., and South, J., Jr., “A Method for Solving the Transonic Full-Potential Equation for General Configurations,” AIAA Paper 83-1889, 1983.
10. Clarke, D., Salas, M., and Hassan, H., “Euler Calculations for Multi-Element Airfoils using Cartesian Grids,” AIAA Journal, vol. 24, 1986.
11. Grossman, B., and Whitaker, D., “Supersonic Flow Computations using a Rectangular-Coordinate Finite-Volume Method,” AIAA Paper 86-0442, 1986.
12. Gaffney, R., Hassan, H., and Salas, M., “Euler Calculations for Wings using Cartesian Grids,” AIAA Paper 87-0356, 1987.
13. Choi, S. K., and Grossman, B., “A Flux-Vector Split, Finite-Volume Method for Euler’s Equations on Non-Mapped Grids,” AIAA Paper 88-0227, 1988.
14. Samant, S. S., Bussoletti, J., Johnson, F., Burkhart, R., Everson, B., Melvin, R., Young, D., Erickson, L., Madson, M., “TRANAIR: A Computer Code for Transonic Analyses of Arbitrary Configurations,” AIAA Paper 87-0034, 1987.
15. LeVeque, R. J., “Cartesian Grid Methods for Flow in Irregular Regions,” Numerical Methods for Fluid Dynamics III; Proceedings of the Conference, Oxford, England, Clarendon Press, 1988, pp. 375-382.
16. Berger, M., and LeVeque, R., “An Adaptive Cartesian Mesh Algorithm for the Euler Equations in Arbitrary Geometries,” AIAA Paper 89-1930, 1989.
17. Berger, M., and LeVeque, R., “Cartesian Meshes and Adaptive Mesh Refinement for Hyperbolic Partial Differential Equations,” Proc. 3rd Intl. Conf. Hyperbolic Problems, Uppsala, Sweden, 1990.
18. Berger, M., and LeVeque, R., “Stable Boundary Conditions for Cartesian Grid Calculations,” ICASE Report No. 90-37, 1990.
19. Bell, J. B., Colella, P., and Welcome, M. L., “Conservative Front-Tracking for Inviscid Compressible Flow,” Proceedings of the AIAA 10th Computational Fluid Dynamics Conference, Honolulu, 1991.
20. Bell, J. B., Berger, M. J., Saltzman, J. S., and Welcome, M. L., “Three Dimensional Adaptive Mesh Refinement for Hyperbolic Conservation Laws,” URCL-JC-108794, LLNL, December 1991.
21. Pember, R. B., Bell, J. B., Colella, P., Crutchfield, W. Y., and Welcome, M. L., “Adaptive Cartesian Grid Methods for Representing Geometry in Inviscid Compressible Flow,” AIAA Paper 93-3385-CP, 1993.
22. De Zeeuw, D., and Powell, K., “An Adaptively-Refined Cartesian Mesh Solver for the Euler Equations,” AIAA Paper 91-1542, 1991.
23. Morinishi, K., “A Finite Difference Solution of the Euler Equations on Non-body-fitted Cartesian Grids,” Computers Fluids, Vol. 21, No. 3, pp.331-344, 1992.
24. Quirk, J., “An Alternative to Unstructured Grids for Computing Gas Dynamic Flows Around Arbitrarily Complex Two-Dimensional Bodies,” ICASE Report 92-7, 1992.
25. Quirk, J., “A Cartesian Grid Approach with Hierarchical Refinement for Compressible Flows,” NASA CR-194938 (ICASE Report 94-51), 1994.
26. Melton, J., Enomoto, F., and Berger, M., “3D Automatic Cartesian Grid Generation for Euler Flows,” AIAA Paper 93-3386-CP, 1993.
27. Tidd, D. M., Strash, D. J., Epstein, B., Luntz, A., Nachson, A., and Rubin, T., “Application of an Efficient 3-D Multigrid Euler Method (MGAERO) to Complete Aircraft Configurations,” AIAA Paper 91-3236, 1991.
28. Karman, S. L. Jr., “SPLITFLOW: A 3D Unstructured Cartesian/Prismatic Grid CFD Code for Complex Geometries,” AIAA Paper 95-0343, 1995.
29. Welterlen, T. J., and Karman, S. L. Jr., “Rapid Assessment of F-16 Store Trajectories Using Unstructured CFD,” AIAA Paper 95-0354, 1995.
30. Melton, J. E., Berger, M. J., Aftosmis, M. J., and Wong, M. D., “3D Applications of a Cartesian Grid Euler Method,” AIAA Paper 95-0853, 1995.
31. Melton, J. E., Berger, M. J., Aftosmis, M. J. And Wong, M. D., “Development and Application of a 3D Cartesian Grid Euler Method,” Surface Modeling, Grid Generation, and Related Issues in Computational Fluid Dynamic (CFD) Solutions, NASA CP-3291, 1995, pp. 225-249.
32. Karman, S. L. Jr., “Unstructured Cartesian/Prismatic Grid Generation for Complex Geometries,” Surface Modeling, Grid Generation, and Related Issues in Computational Fluid Dynamic (CFD) Solutions, NASA CP-3291, 1995, pp. 251-270.
33. W. F. Ames, “Numerical Methods for Partial Differential Equations”, Academic Press, New York (1977).
34. O. C. Zienkiewicz, and R. L. Taylor, “The Finite Element Method”, McGRAW-Hill (1989).
35. R. Y. Chang, and W. H. Yang, “Numerical Simulation of Mold Filling in Injection Molding Using a Three-Dimensional Finite Volume Approach”, submitted to Int. J. Numer. Methods Fluids (2000).
36. C. M. Rhie and W. L. Chow, “A Numerical Study of the Turbulent Flow Past an Isolated Airfoil with Trailing Edge Separation”, AIAA J., 21, 1525 (1983).
37. Jinn-Liang Liu, Ing-Jer Lin, Minn-Zhih Shih, Ren-Chuen Chen, Mao-Chung Hsieh, “Object-oriented programming of adaptive finite element and finite volume methoed”, Applied Numerical Mathematics, 21, 439-467, (1996).
38. O’Rourke, J. “Computational Geometry in C”, Cambridge University Press, 1994.