Automated approach to very high-order aeroacoustic computations

AIAA journal

Volumn 39, Issue 3, 2001, Pages 396-406

  Dyson, Rodger W ^a   Goodrich, John W ^a  

^a NASA GLENN RESEARCH CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTIC NOISE; ACOUSTIC WAVE PROPAGATION; COMPUTATIONAL COMPLEXITY; COMPUTER SIMULATION; INTERPOLATION; LINEAR EQUATIONS;

CARTESIAN GRIDS; CAUCHY-KOWALEWSKI RECURSION PROCEDURE; COMPUTATIONAL AEROACOUSTICS;

AERODYNAMICS;

EID: 0035281080     PISSN: 00011452     EISSN: None     Source Type: Journal    
DOI: 10.2514/2.1349     Document Type: Article

References (41)

1. Lele, S. K., "Computational Aeroacoustics: A Review," AIAA Paper 97-0018, Jan. 1997.
2. Tam, C. K. W., "Computational Aeroacoustics: Issues and Methods," AIAA Journal, Vol. 33, No. 10, 1995, pp. 1788-1796.
3. Vemuri, V., and Karplus, W., "Higher-Order Difference Approximations." Digital Computer Treatment of Partial Differential Equations, Prentice-Hall, Upper Saddle River, NJ, 1981, pp. 92-98.
4. Goodrich, J. W., "High Order Implementations of Accurate Boundary Conditions," AIAA Paper 99-1942, May 1999.
5. Tam, C. K. W., "Advances in Numerical Boundary Conditions for Computational Aeroacoustics," AIAA Paper 97-1774, 1997.
6. Carpenter, M. H., Nordstrom, J., and Gottlieb, D., "A Stable and Conservative Interface Treatment of Arbitrary Spatial Accuracy," Inst. for Computer Applications in Science and Engineering, ICASERept. 98-12, Hampton. VA. Feb. 1998.
7. Carpeneter, M. H., and Casper, J. H., "The Accuracy of Shock Capturing in Two Spatial Dimensions." AIAA Paper 97-2107, July 1997.
8. Goodrich, J. W., "A Low Order and a High Order Solution For A Converging-Diverging Nozzle Problem," Third Computational Aeroacoustics Workshop. NASA CP 2000-209-790, Aug. 2000.
9. Woodward, P., and Collela, P., "The Numerical Solution of Two- Dimensional Fluid Flow with Strong Shocks." Journal of Computational Physics, Vol. 54, No. 1, 1984. pp. 115-173.
10. Casper, J., and Carpeneter, M. H., "Computational Considerations for the Simulation of Shock-Induced Sound." SIAM Journal of Scientific and Statistical Computation, Vol. 19, No. 3, 1998, pp. 813-828.
11. Goodrich, J. W., "High Accuracy Finite Difference Algorithms for Computational Aeroacoustics," AIAA Paper 97-1584, May 1997.
12. Lee,T. K., and Zhong, X., "Spurious Numerical Oscillations in Simulation of Supersonic Flows Using Schock-Capturing Schemes," AIAA Journal, Vol. 37, No. 3, 1999, pp. 313-319.
13. Lockard, D. P., Brentner, K. S., and Atkins, H. L., "High-Accuracy Algorithms for Computational Aeroacoustics," AIAA Journal, Vol. 33, No. 2, 1995, pp. 246-251.
14. Tam, C. K. W., and Dong, Z., "Wall Boundary Conditions for High-Order Finite-Difference Schemes in Computational Aeroacoustics," Theoretical Computational Fluid Dynamics, Vol. 6, 1994, pp. 303-322.
15. Strand, B., "Simulations of Acoustic Wave Phenomena Using High-Order Finite Difference Approximations." SIAM Journal of Scientific and Statistical Computation, Vol. 20, No. 5, 1999, pp. 1585-1604.
16. Butcher, J. C., "The Non-Existence of Ten Stage Eighth Order Explicit Runge-Kutta Methods," BIT, Vol. 25, No. 3, 1985, pp. 521-540.
17. Buchberger, B., "Gröebner Bases in Mathematica: Enthusiam and Frustration" RISC-Linz Technical Rept. Series No. 91-11, Linz, Austria, 1991.
18. Cox, D., Little, J., and O'Shea, D., Ideals, Varieties, and Algorithms, 2nd ed., Springer-Verlag, 1996, Chaps. 1,2.
19. Mayr, K., and Meyer, A., "The Complexity of the Word Problem for Commutative Semigroups and Polynomial Ideals," Advanced Mathematics, Vol. 46, No. 3, 1982. pp. 305-329.
20. Wolfram Research, "Numerical Mathematics," Mathematica 4.0: Standard Add-On Packages, Wolfram Media.Champaign. IL, 1999, pp. 354-363.
21. Sofroniou, M., "Symbolic Derivation of Runge-Kutta Methods," Journal of Symbolic Computation, Vol. 18, No. 3, 1994, pp. 265-296.
22. Stanescu, D., and Habashi, W. G., "2N-Storage Low Dissipation and Dispersion Runge-Kutla Schemes for Computational Acoustics." Journal of Computational Physics. Vol 143, No. 2, 1998, p. 674.
23. Goodrich, J. W., "A Comparison of Numerical Methods for Computational Aeroacoustics." AIAA Paper 99-1943, May 1999.
24. Goodrich, J. W., "Application of a New High Order Finite Difference Scheme to Acoustic Propagation With the Linearized Euler Equation." NASA TM-1993-106454, June 1993.
25. Goodrich, J. W., "Accurate Finite Difference Algorithms for Computational Aeroacoustics," Computational Fluid Dynamics Review 1998, edited by M. M Hafez and K. Oshima, Vol. 2, World Scientific, Singapore, 1998, pp. 1034-1051.
26. Garabedian, P. R., "The Method of Power Series: The Cauchy-Kowalewski Theorem," Partial Differential Equations, 2nd ed., Chelsea, New York, 1986, pp. 6-16.
27. Dyson, R. W., and Goodrich, J. W., "A Very High Order, Adaptable MESA Implementation for Aeroacoustic Computations." NASA TM-2000-209944, April 2000.
28. Botha, J. F., and Pinder, G. F., "Two-Dimensional Polynomial Approximation," Fundamental Concepts in the Numerical Solution of Differential Equations, Wiley, New York, 1983, pp. 17-22.
29. Dyson, R. W., "An Automated Code Generator For Three-Dimensional Acoustic Wave Propagation With Geometrically Complex Solid Wall Boundaries," Ph.D. Dissertation, Computer Engineering Dept., Case Western Reserve Univ., Cleveland. OH, May 1999; also NASA TM-1999-209182, 1999.
30. Berger, M. J., and Leveque, R. J., "Adaptive Mesh Refinement Using Wave-Propagation Algorithms for Hyperbolic Systems," SIAM Journal on Numerical Analysis, Vol. 35, No. 6, 1998, pp. 2298-2316.
31. Kurbatskii, K. A., and Tam, C. K. W., "Cartesian Boundary Treatment of Curved Walls for High-Order Computational Aeroacoustics Schemes." AIAA Journal, Vol. 35, No. 1, 1997, pp. 133-140.
32. Wirth, M. C., "On the Automation of Computational Physics," Ph.D. Dissertation, Engineering-Applied Science, Univ. of California Davis CA Sept. 1980.
33. Steinberg, S., and Roache, P., "Automatic Generation of Finite Difference Code," Symbolic Computation in Fluid Mechanics and Heat Transfer, edited by H. H. Bau, T. Herbert, and M. M Yovanovich, American Society of Mechanical Engineers, Fairfield, NJ, 1988, p. 81.
34. Goodrich, J. W., "An Approach to the Development of Numerical Algorithms for First Order Linear Hyperbolic Systems in Multiple Space Dimensions: The Constant Coefficient Case," NASA TM-1995-106928, Sept. 1995.
35. Powell, M. J. D., "Hermite Interpolation." Approximation Theory and Methods, Cambridge Univ. Press, Cambridge, England, U.K., 1981, pp. 57.
36. Lax, P. D., and Wendroff, B., "Systems of Conservation Laws," Communications on Pure and Applied Mathematics, Vol. 13, No. 2, 1960, pp. 217-237.
37. Fulks, W., "The Gradient. The Del Operator. Directional Derivatives," Advanced Calculus: An Introduction to Analysis, Wiley, New York, 1978 pp. 315-320.
38. Zauderer, E., "Classification of Equations in General and their Characteristics," Partial Differential Equations of Applied Mathematics, 2nd ed., Wiley, New York, 1989, pp. 121-136.
39. Winston, P. H., "Propagating Symbolic Constraints," Artificial Intelligence, Addison Wesley Longman, Reading, MA, 1984, pp. 46-71.
40. Sklar, B., "The Sampling Theorem," Digital Communications: Fundamentals and Applications, Prentice-Hall, Upper Saddle River, NJ, 1988, pp. 59, 60.
41. Hildebrand, F. B., Introduction to Numerical Analysis, McGraw-Hill, New York, 1956, pp. 35-175.