Maintaining the stability of a leapfrog scheme in the presence of source terms

International Journal for Numerical Methods in Fluids

Volumn 42, Issue 8, 2003, Pages 839-852

  Kim, Cheolwan ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Leapfrog; Non dissipative; Stability; Transformation; Upwind

Indexed keywords

ACOUSTICS; MATHEMATICAL TRANSFORMATIONS; NUMERICAL METHODS;

LEAPFROG SCHEME;

FLUID DYNAMICS;

ACOUSTICS;

EID: 0037998475     PISSN: 02712091     EISSN: None     Source Type: Journal    
DOI: 10.1002/fld.549     Document Type: Article

References (10)

1. Davis S. Low-dispersion finite difference methods for acoustic waves in a pipe. Journal of the Acoustical Society of America 1991; 90(5):2775-2781.
2. Haras Z, Ta'asan S. Finite-difference schemes for long-time integration. Journal of Computational Physics 1994; 114:265-279.
3. Hu FQ, Hussaini MY, Manthey J. Low-dissipation and dispersion Runge-Kutta schemes for computational acoustics. Journal of Computational Physics 1996; 124:177-191.
4. Kopriva DA. Spectral solution of the time dependent Euler gasdynamics equations. AIAA Paper DGLR/AIAA-92-02-036 (DGLR/AIAA 14th Aeroacoustics Conference), 1992.
5. Lele SK. Compact finite difference schemes with spectral-like resolution. Journal of Computational Physics 1991; 103:16-42.
6. Tam CKW, Webb JC. Dispersion-relation-preserving finite difference schemes for computational acoustics. Journal of Computational Physics 1992; 107:262-281.
7. Zingg DW, Lomax H, Jurgens HM. High accuracy finite-difference scheme for linear wave propagation. SIAM Journal on Scientific Computing 1996; 17:328-346.
8. Thomas JP, Roe PL. Development of non-dissipative numerical schemes for computational aeroacoustics. AIAA Paper 93-3382 (AIAA 11th Computational Fluid Dynamics Conference), 1993.
9. Roe PL. Linear bicharacteristic schemes without dissipation. SIAM Journal of Scientific Computing 19(5).
10. Tam CKW, Hardin JC. (eds). Second Computational Aeroacoustics (CAA) Workshop on Benchmark Problems, NASA Conference Paper 3352, June 1997.