Free Access
Issue
ESAIM: M2AN
Volume 49, Number 1, January-February 2015
Page(s) 39 - 67
DOI https://doi.org/10.1051/m2an/2014024
Published online 12 January 2015
  1. M. Carpenter, D. Gottlieb and S. Abarbanel, Time-stable conditions for finite-difference schemes solving hyperbolic systems: methodology and application to high-order compact schemes. J. Comput. Phys. 111 (1994) 220–236. [CrossRef] [Google Scholar]
  2. M. Carpenter, J. Nordström and D. Gottlieb, A stable and conservative interface treatment of arbitrary spatial accuracy. J. Comput. Phys. 148 (1999) 341–365. [CrossRef] [Google Scholar]
  3. G.S. Constantinescu and S.K. Lele, Large eddy simulation of a near sonic turbulent jet and its radiated noise. AIAA Paper 0376 (2001). [Google Scholar]
  4. M. Goldberg, On a boundary extrapolation theorem by Kreiss. Math. Comput. 31 (1977) 469–477. [CrossRef] [Google Scholar]
  5. M. Goldberg and E. Tadmor, Scheme-independent stability criteria for difference approximations of hyperbolic initial-boundary value problems. I. Math. Comput. 32 (1978) 1097–1107. [CrossRef] [Google Scholar]
  6. M. Goldberg and E. Tadmor, Scheme-independent stability criteria for difference approximations of hyperbolic initial-boundary value problems. II. Math. Comput. 36 (1981) 603–626. [CrossRef] [Google Scholar]
  7. B. Gustafsson, On the implementation of boundary conditions for the methode of lines. BIT 38 (1998) 293–314. [CrossRef] [MathSciNet] [Google Scholar]
  8. B. Gustafsson, H.-O. Kreiss and J. Oliger, Time dependent problems and difference methods. John Wiley & Sons (1995). [Google Scholar]
  9. B. Gustafsson, H.-O. Kreiss and A. Sundström, Stability theory of difference approximations for mixed initial boundary value problem. II. Math. Comput. 26 (1972) 649–686. [CrossRef] [Google Scholar]
  10. H.-O. Kreiss and G. Scherer, Finite element and finite difference methods for hyperbolic partial differential operators. Mathematical aspects of finite elements in partial differential equations. Academic Press, Orlando, FL (1974). [Google Scholar]
  11. H.-O. Kreiss and G. Scherer, On the existence of energy estimates for difference approximations for hyperbolic systems. Technical report, Uppsala University, Sweden (1977). [Google Scholar]
  12. S. Lee, S.K. Lele and P. Moin, Interaction of isotropic turbulence with shock waves: effect of shock strength. J. Fluid Mech. 340 (1997) 225–247. [CrossRef] [Google Scholar]
  13. S.K. Lele, Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103 (1992) 16–42. [NASA ADS] [CrossRef] [Google Scholar]
  14. X. Liu, S. Zhang, H. Zhang and C.-W. Shu, A new class of central compact schemes with spectral-like resolution I: linear schemes. J. Comput. Phys. 248 (2013) 235–256. [CrossRef] [Google Scholar]
  15. K. Mahesh, S.K. Lele and P. Moin, The influence of entropy fluctuation on the interaction of turbulence with a shock wave. J. Fluid Mech. 334 (1997) 353–379. [CrossRef] [Google Scholar]
  16. K. Mattsson, Boundary procedure for summation-by-parts operators. J. Sci. Comput. 18 (2003) 133–153. [CrossRef] [Google Scholar]
  17. K. Mattsson and J. Nordström, Summation by parts operators for finite difference approximations of second derivatives. J. Comput. Phys. 199 (2004) 503–540. [CrossRef] [Google Scholar]
  18. P. Moin, K. Squires, W. Cabot and S. Lee, A dynamic subgridscale model for compressible turbulence and scalar transport. Phys. Fluid 3 (1991) 2746–2757. [Google Scholar]
  19. P. Olson, Summation by parts, projection and stability: I. Math. Comput. 64 (1995) 1035–1065. [CrossRef] [Google Scholar]
  20. C.-W. Shu and S. Osher, Efficient implementation of essentially non-oscillatory shock-capturing schemes. J. Comput. Phys. 77 (1988) 439–471. [Google Scholar]
  21. B. Strand, Summation by parts for finite difference approximations for d/dx. J. Comput. Phys. 110 (1994) 47–67. [CrossRef] [Google Scholar]
  22. J.C. Strikwerda, Initial boundary value problems for the method of lines. J. Comput. Phys. 34 (1980) 94–107. [CrossRef] [Google Scholar]
  23. S. Tan and C.-W. Shu, Inverse Lax−Wendroff procedure for numerical boundary conditions of conservations laws. J. Comput. Phys. 229 (2010) 8144–8166. [CrossRef] [Google Scholar]
  24. S. Tan, C. Wang, C.-W. Shu and J. Ning, Efficient implementation of high order inverse Lax−Wendroff boundary treatment for conservation laws. J. Comput. Phys. 231 (2012) 2510–2527. [CrossRef] [Google Scholar]

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