Strictly stable high order difference approximations for the euler equations

Proceedings of the Tenth International Congress on Sound and Vibration

Volumn , Issue , 2003, Pages 3883-3890

  Müller, Bernhard ^a   Johansson, Stefan ^a  

^a UPPSALA UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTIC NOISE; ACOUSTIC WAVE PROPAGATION; AERODYNAMICS; APPROXIMATION THEORY; COMPUTATIONAL METHODS; COMPUTER SIMULATION; DEFORMATION; INFORMATION TECHNOLOGY; INITIAL VALUE PROBLEMS; LAUNCHING; MATHEMATICAL MODELS; NAVIER STOKES EQUATIONS; NONLINEAR EQUATIONS; ROCKETS;

COMPUTATIONAL AEROACOUSTICS (CAA); EULER EQUATIONS; KIRCHHOFF VORTEX; MACH NUMBERS;

DIFFERENCE EQUATIONS;

EID: 18144440990     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (26)

1. M.H. Carpenter, D. Gottlieb, S. Abarbanel: Time-Stable Boundary Conditions for Finite-Difference Schemes Solving Hyperbolic Systems: Methodology and Application to High-Order Compact Schemes. J. Comput. Physics, 111, 220-236 (1994)
2. B. Fornberg: A Practical Guide to Pseudospectral Methods. First Paperback Edition, Cambridge University Press, Cambridge, 1998.
3. B. Gustafsson, H.-.O Kreiss, J. Oliger: Time Dependent Problems and Difference Methods. John Wiley & Sons, New York, 1995.
4. M. Gerritsen, P. Olsson: Designing an Efficient Solution Strategy for Fluid Flows. J. Comput. Physics, 129, 245-262 (1996).
5. J.C. Hardin, J.R. Ristorcelli, C.K.W. Tam (Editors): ICASE/LaRC Workshop on Benchmark Problems in Computational Aeroacoustics (CAA). NASA Conference Publication 3300 (1995)
6. S. Johansson: Numerical Solution of the Linearized Euler Equations Using High Order Finite Difference Operators with the Summation by Parts Property. Technical Report 2002-034, Department of Information Technology, Uppsala University, Oct. 2002, http://www.it.uu.se/research/reports/.
7. H.-O. Kreiss, G. Scherer: Finite Element and Finite Difference Methods for Hyperbolic Partial Differential Equations. Mathematical Aspects of Finite Elements in Partial Differential Equations, Academic Press, New York (1974)
8. B. Müller: On Sound Generation by the Kirchhoff Vortex. Report No. 209/ 1998, Dept. of Scientific Computing, Uppsala University, 1998, http://www.it.uu.se/research/reports/.
9. B. Müller: High Order Difference Method for Low Mach Number Aeroacoustics. ECCOMAS Computational Fluid Dynamics Conference, Swansea, Wales, UK (2001)
10. B. Müller J. Westerlund: High Order Numerical Simulation of Rocket Launch Noise. Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation, Jyväskylä, Finland, June 30 - July 4, 2003.
11. B. Müller, H.C. Yee: High Order Numerical Simulation of Sound Generation by the Kirchhoff Vortex. Computing and Visualization in Science, Vol. 4, pp. 197-204, 2002; also published as Technical Report 2001-004, Department of Information Technology, Uppsala University, Febr. 2001; and RIACS Technical Report 01.02, Jan. 2001, NASA Ames Research Center.
12. B. Müller, H.C. Yee: High Order Numerical Simulation of Sound Generation by the Kirchhoff Vortex. Computing and Visualization in Science, Vol. 4, pp. 197-204, 2002; also published as Technical Report 2001-004, Department of Information Technology, Uppsala University, Febr. 2001; and RIACS Technical Report 01.02, Jan. 2001, NASA Ames Research Center.
13. B. Müller, H.C. Yee: High Order Numerical Simulation of Sound Generation by the Kirchhoff Vortex. Computing and Visualization in Science, Vol. 4, pp. 197-204, 2002; also published as Technical Report 2001-004, Department of Information Technology, Uppsala University, Febr. 2001; and RIACS Technical Report 01.02, Jan. 2001, NASA Ames Research Center.
14. B. Müller, H.C. Yee: Entropy Splitting for High Order Numerical Simulation of Vortex Sound at Low Mach Numbers. Proceedings of the Fifth International Conference On Spectral and High Order Methods (ICOSAHOM-01, Uppsala, 11-15 June 2001), Journal of Scientific Computing, Vol. 17, No.s 1-4, Dec. 2002, pp. 181-190; also published as RIACS Technical Report 01.23, 2001, NASA Ames Research Center.
15. B. Müller, H.C. Yee: Entropy Splitting for High Order Numerical Simulation of Vortex Sound at Low Mach Numbers. Proceedings of the Fifth International Conference On Spectral and High Order Methods (ICOSAHOM-01, Uppsala, 11-15 June 2001), Journal of Scientific Computing, Vol. 17, No.s 1-4, Dec. 2002, pp. 181-190; also published as RIACS Technical Report 01.23, 2001, NASA Ames Research Center.
16. B. Müller, H.C. Yee: Entropy Splitting for High Order Numerical Simulation of Vortex Sound at Low Mach Numbers. Proceedings of the Fifth International Conference On Spectral and High Order Methods (ICOSAHOM-01, Uppsala, 11-15 June 2001), Journal of Scientific Computing, Vol. 17, No.s 1-4, Dec. 2002, pp. 181-190; also published as RIACS Technical Report 01.23, 2001, NASA Ames Research Center.
17. J. Nordström, M.H. Carpenter: Boundary and Interface Conditions for High-Order Finite-Difference Methods Applied to the Euler and Navier-Stokes Equations. J. Comput. Physics, 148, 621-645 (1999)
18. P. Olsson: Summation by Parts, Projections and Stability. III. RIACS Technical Report 95.06, 1995.
19. P. Olsson, J. Oliger: Energy and Maximum Norm Estimates for Nonlinear Conservation Laws. RIACS Technical Report 94.01, 1994.
20. W. Polifke, B. Müller, H.C. Yee: Sound Emission of Rotor Induced Deformations of Generator Casings AIAA Paper 2001-2274, 7th AIAA/CEAS Aeroacoustics Conference, May 28-30, 2001/Maastricht, The Netherlands. RIACS Technical Report 01.04, March 2001.
21. J. Sesterhenn, B. Müller, H. Thomann: On the Cancellation Problem in Calculating Compressible Low Mach Number Flows. J. Comput. Physics, 151, 597-615 (1999).
22. B. Strand: Summation by Parts for Finite Difference Approximations for d/dx. J. Comput. Physics, 110, 47-67 (1994)
23. B. Strand: Simulations of Acoustic Wave Phenomena Using High-Order Finite Difference Approximations. SIAM J. Sci. Comput., 20, 1585-1604 (1999).
24. C.K.W. Tam: Computational Aeroacoustics: Issues and Methods. AIAA J., 33, 1788-1796 (1995).
25. R. Vichnevetsky, J.B. Bowles: Fourier Analysis, of Numerical Approximations of Hyperbolic Equations. SIAM, Philadelphia, 1982.
26. J. Westerlund: High Order Simulation of Rocket Launch Noise. Master's Thesis, Uppsala University, Sweden (2002)