Steady-state computations using summation-by-parts operators

Journal of Scientific Computing

Volumn 24, Issue 1, 2005, Pages 647-663

  Svärd, Magnus ^a   Mattsson, Ken ^a   Nordström, Jan ^a,b  

^a UPPSALA UNIVERSITY   (Sweden)

^b SWEDISH DEFENCE RESEARCH AGENCY   (Sweden)

Author keywords

Convergence to steady state; High order finite differences; Stability; Summation by parts operators

Indexed keywords

BOUNDARY CONDITIONS; CONVERGENCE OF NUMERICAL METHODS; FINITE DIFFERENCE METHOD; MATHEMATICAL OPERATORS; PROBLEM SOLVING; SYSTEM STABILITY;

CONVERGENCE TO STEADY STATE; HIGH ORDER FINITE DIFFERENCES; STEADY-STATE COMPUTATIONS; SUMMATION-BY-PARTS OPERATORS;

COMPUTATIONAL METHODS;

EID: 23244468172     PISSN: 08857474     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10915-004-4788-2     Document Type: Article

References (15)

1. Mattsson, K., Svärd, M., Nordström, J., and Carpenter, M. H. (2003). Accuracy Requirements for Transient Aerodynamics AIAA paper 2003-3689.
2. Zingg, D. W. (2000) Comparison of high-accuracy finite-difference methods for linear wave propagation. SIAM J. Sci. Comput. 22, 476-502.
3. Zingg, D. W., De Rango, S., Memec, M., and Pulliam, T. H. (2000). Comparison of Several Spatial Discretizations for the Navier-Stokes equations. J. Comput. Phys. 160, 683-704.
4. Kreiss, H.-O., and Scherer, G. (1974). Finite element and finite difference methods for hyperbolic partial differential equations. Mathematical Aspects of Finite Elements in Partial Differential Equations, Academic Press Inc. New York.
5. Kreiss, H.-O. and Scherer, G. (1977). On the existence of energy estimates for difference approximations for hyperbolic systems Technical report, Dept. of Scientific Computing Uppsala University.
6. Svärd, M. (2004). On coordinate transformations for summation-by-parts operators. J. Sci. Comput. 20(1), 29-42.
7. Mattsson, K., Svärd, M. and Nordström, J. (2004). Stable and Accurate Artificial Dissipation. J. Sci. Comput. 21(1), 57-79.
8. Carpenter, M. H., Gottlieb, D., and Abarbanel, S. (1994). The stability of numerical boundary treatments for compact high-order finite-difference schemes. J. Comput. Phys. 108(2), 272-295.
9. Carpenter, M. H., Nordström, J. and Gottlieb, D. (1999). A Stable and Conservative interface treatment of Arbitrary Spatial Accuracy. J. Comput. Phys. 148, 341-365.
10. Nordström, J., and Carpenter, M. H. (1999) Boundary and interface conditions for high order finite difference methods applied to the Euler and Navier-Stokes equations J. Comput. Phys. 148, 621-645.
11. Nordström, J. and Carpenter, M. H. (2001). High-order finite difference methods multi-dimensional linear problems and curvilinear coordinates. J. Comput. Phys. 173, 149-174.
12. Strand, B. (1994). Summation by parts for finite difference approximations for d/dx. J. Comput. Phys. 110, 46-67.
13. Zingg, D. W. (1997). Aspect of linear stability amalysis for higher-order finite-difference methods. AIAA paper 1997-1939.
14. Gustafsson, B., Kreiss, H.-O., and Oliger, J., (1995). Time Dependent Problems and Difference Methods. Wiley, New York.
15. Jurgens, H. M., and Zingg, D. W. (2000). Numerical solution of the time-domain max-well equation using high-accuracy finite-difference methods. SIAM J. Sci. Comput. 22, 1675-1696.