A general strategy for the optimization of Runge-Kutta schemes for wave propagation phenomena

Journal of Computational Physics

Volumn 228, Issue 11, 2009, Pages 4182-4199

  Bernardini, Matteo ^a   Pirozzoli, Sergio ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Computational aeroacoustics; Numerical dispersion; Numerical dissipation; Optimized algorithms; Runge Kutta schemes

Indexed keywords

COMPUTATION THEORY; COMPUTATIONAL AEROACOUSTICS; COMPUTATIONAL FLUID DYNAMICS; FINITE DIFFERENCE METHOD; WAVE PROPAGATION;

FINITE DIFFERENCE SCHEME; NUMERICAL DISPERSIONS; NUMERICAL DISSIPATION; OPTIMISATIONS; OPTIMIZED ALGORITHMS; PERFORMANCE; PERFORMANCE ANALYSIS AND OPTIMIZATIONS; RUNGE-KUTTA SCHEMES; TIME-INTEGRATION SCHEME; WAVE PROPAGATION PROBLEMS;

RUNGE KUTTA METHODS;

EID: 64049087583     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2009.02.032     Document Type: Article

References (18)

1. Pirozzoli S. Performance analysis and optimization of finite-difference schemes for wave propagation problems. J. Comput. Phys. 222 (2007) 809-831
2. Williamson J.H. Low-storage Runge-Kutta schemes. J. Comput. Phys. 35 (1980) 48-56
3. Lele S.K. Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103 (1992) 16-42
4. Tam C.K.W., and Webb J.C. Dispersion-relation-preserving finite difference scheme for computational acoustics. J. Comput. Phys. 107 (1993) 262-281
5. Kim J., and Lee D. Optimized compact finite difference schemes with maximum resolution. AIAA J. 34 5 (1996) 887-893
6. C. Lui, S.K. Lele, Direct numerical simulation of spatially developing, compressible, turbulent mixing layers, AIAA Paper 2001-0291.
7. Butcher J.C. The Numerical Analysis of Ordinary Differential Equations (1987), Wiley, Chichester
8. Hu F.Q., Hussaini M.Y., and Manthey J.L. Low-dissipation and low-dispersion Runge-Kutta schemes for computational acoustics. J. Comput. Phys. 124 (1996) 177-191
9. Kennedy C.A., Carpenter M.H., and Lewis R.M. Low-storage, explicit Runge-Kutta schemes for the compressible Navier-Stokes equations. Appl. Numer. Math. 35 (2000) 177-219
10. Stanescu D., and Habashi W.G. 2 n-storage low dissipation and dispersion Runge-Kutta schemes for computational acoustics. J. Comput. Phys. 143 (1998) 674-681
11. Calvo M., Franco J.M., and Rández L. Minimum storage Runge-Kutta schemes for computational acoustics. Comput. Math. Appl. 45 (2003) 535-545
12. Calvo M., Franco J.M., and Rández L. A new minimum storage Runge-Kutta scheme for computational acoustics. J. Comput. Phys. 201 (2004) 1-12
13. Bogey C., and Bailly C. A family of low dispersive and low dissipative explicit schemes for flow and noise computations. J. Comput. Phys. 194 (2004) 194-214
14. Berland J., Bogey C., and Bailly C. Low-dissipation and low-dispersion fourth-order Runge-Kutta algorithm. Comput. Fluids 35 (2006) 1459-1463
15. Ramboer J., Broeckhoven T., Smirnov S., and Lacor C. Optimization of time integration schemes coupled to spatial discretization for use in CAA applications. J. Comput. Phys. 213 (2006) 777-802
16. Hirsch C. Numerical Computation of Internal and External Flows (1988), Wiley, New York
17. J.C. Hardin, J.R. Ristorcelli, C.K.W. Tam (Eds.), ICASE/LaRC Workshop on Benchmark Problems in Computational Aeroacoustics, NASA CP 3300, 2005.
18. Bogey C., Bailly C., and Juvé D. Computation of flow noise using source terms in linearized Euler's equations. AIAA J. 40 (2002) 235-243