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International Journal of Computer Mathematics Volume 88, 2011 - Issue 12
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Section B

Spurious caustics of dispersion-relation-preserving schemes

Claire David Institut Jean Le Rond d'Alembert, UMR CNRS 7190, Université Pierre et Marie Curie-Paris 6, Boîte courrier no 162, 4 place Jussieu, F-75252, Paris Cedex 05, FranceCorrespondence[email protected]
&
Pierre Sagaut Institut Jean Le Rond d'Alembert, UMR CNRS 7190, Université Pierre et Marie Curie-Paris 6, Boîte courrier no 162, 4 place Jussieu, F-75252, Paris Cedex 05, France
Pages 2625-2636 | Received 26 Oct 2008, Accepted 22 Dec 2010, Published online: 25 May 2011

References

  • Burgers , J. M. 1939 . Mathematical examples illustrating relations occurring in the theory of turbulent fluid motion . Trans. R. Neth. Acad. Sci. Amsterdam , 17 : 1 – 53 .
  • David , Cl. , Sagaut , p. and Sengupta , T. 2009 . A linear dispersive mechanism for numerical error growth: Spurious caustics . Eur. J. Fluid Mech. , 28 ( 1 ) : 146 – 151 .
  • Hirsch , C. 1988 . Numerical Computation of Internal and External Flows , New York : Wiley-Interscience .
  • Hoarau , E. , David , Cl. , Sagaut , P. and Lê , T.-H. 2007 . Lie group study of finite difference schemes . Discrete Contin. Dyn. Syst. , 14 : 180 – 184 .
  • Leonard , B. P. , Lock , A. P. and Macvean , M. K. 1995 . The NIRVANA scheme applied to one-dimensional advection . Int. J. Numer. Methods Heat Fluid Flow , 5 : 341 – 377 .
  • Leonard , B. P. , Lock , A. P. and Macvean , M. K. 1996 . Conservative explicit unrestricted-time-step multidimensional constancy-preserving advection schemes . Monthly Weather Rev. , 124 : 2588 – 2606 .
  • Lomax , H. , Pulliam , T. H. and Zingg , D. W. 2002 . Fundamentals of Computational Fluid Dynamics , Berlin : Springer .
  • Sengupta , T. K. 2004 . Fundamentals of Computational Fluid Dynamics , Hyderabad, (India) : Hyderabad University Press .
  • Sengupta , T. K. and Dipankar , A. 2004 . A comparative study of time advancement methods for solving Navier–Stokes equations . J. Sci. Comput. , 21 ( 2 ) : 225 – 250 .
  • Sengupta , T. K. , Sircar , S. K. and Dipankar , A. 2006 . High accuracy schemes for DNS and acoustics . J. Sci. Comput. , 26 ( 2 ) : 151 – 193 .
  • Tam , C. K. and Webb , J. C. 1993 . Dispersion-relation-preserving finite difference schemes for computational acoustics . J. Comput. Phys. , 107 : 262 – 281 .
  • Vichnevetsky , R. and Bowles , J. B. 1982 . Fourier analysis of numerical approximations of hyperbolic equations . SIAM Stud. Appl. Math. , 5
  • Witham , G. B. 1974 . Linear and Nonlinear Wave , New York : Wiley-Interscience .
  • Zingg , D. W. 2000 . Comparison of high-accuracy finite-difference methods for linear wave propagation . SIAM J. Sci. Comput. , 22 : 227 – 238 .

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