A new shock/discontinuity detector

References

• Archibald, R. , Gelb, A. , and Yoon, J. , 2008. Determining the locations and discontinuities in the derivatives of functions , Appl. Numer. Math. 58 (2008), pp. 577–592.
   Web of Science ®Google Scholar
• Cueto-Felgueroso, L. , Colominas, I. , Noguira, X. , Navarrina, F. , and Casteleiro, M. , 2007. Finite volume solvers and moving least-squares approximations for the compressible Navier–Stokes equations on unstructured grid , Comput. Methods Appl. Mech. Engrg. 196 (2007), pp. 4712–4736.
   Web of Science ®Google Scholar
• Degrez, G. , Boccadoro, C. H. , and Wendt, J. F. , 1987. The interaction of an oblique shock wave with a laminar boundary layer revisited: An experimental numerical study , J. Fluid Mech. 177 (1987), pp. 247–263.
   Web of Science ®Google Scholar
• Godnov, S. K. , 1969. A difference scheme for numerical computation of discontinuous solution of hydrodynamic equations , Math Sbornik 47 (1969), pp. 271–306, (in Russian) translated US Joint Publ. Res. Service, JPRS 7226.
   Google Scholar
• Harten, A. , 1978. The artificial compression method for computation of shocks and contact discontinuities: III. self-adjusting hybrid schemes , Math. Comp. 32 (142) (1978), pp. 363–389.
   Web of Science ®Google Scholar
• Harten, A. , 1983. High resolution schemes for hyperbolic conservation laws , J. Comput. Phys. 49 (1983), pp. 357–393.
   Web of Science ®Google Scholar
• Harten, A. , Engquist, B. , Osher, B. , and Charkravarthy, S. R. , 1987. Uniformly high order accurate essentially non-oscillatory schemes III , J. Comput. Phys 71 (1987), pp. 231–303, 1987.
   Web of Science ®Google Scholar
• Jameson, A. , Schmidt, W. , and Turkel, E. , 1981. Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes , AIAA paper (1981), pp. 1981–1259.
   Google Scholar
• Jiang, L. , Shan, H. , and Liu, C. , 2001. Weight compact scheme for shock capturing , Int. J. Comput. Fluid Dyn. 15 (2001), pp. 147–155.
   Web of Science ®Google Scholar
• Jiang, G. S. , and Shu, C. W. , 1996. Efficient implementation of weighted ENO scheme , J. Comput. Phys. 126 (1996), pp. 202–228.
   Web of Science ®Google Scholar
• Lele, S. K. , 1992. Compact finite difference schemes with spectral-like resolution , J. Comput. Phys. 103 (1992), pp. 16–42.
   Web of Science ®Google Scholar
• Liu, D. , Osher, S. , and Chan, T. , 1994. Weighted essentially nonoscilltory schemes , J. Comput. Phys. V115 (1994), pp. 200–212.
   Google Scholar
• Martin, M. P. , 2007. Direct numerical simulation of hypersonic turbulent boundary layers. Part 1. Initialization and Comparison With Experiments , J. Fluid Mech. 570 (2007), pp. 347–364.
   Web of Science ®Google Scholar
• Roe, P. L. , Approximate Riemann solvers, parameter vectors and difference schemes , J. Comput. Phys. 43, pp. 357–372.
   Web of Science ®Google Scholar
• Shu, C. W. , and Osher, S. , 1988. Efficient implementation of essentially non-oscillatory shock-capturing scheme , J. Comput. Phys. 77 (1988), pp. 439–471.
   Web of Science ®Google Scholar
• Shu, C. W. , and Osher, S. , 1989. Efficient implementation of essentially non-oscillatory shock-capturing schemes II , J. Comput. Phys 83 (1989), pp. 32–78.
   Web of Science ®Google Scholar
• Van Leer, B. , 1979. Towards the ultimate conservative difference scheme. V: A second-order sequel to Godnov's scheme , J. Comput. Phys. 32 (1979), pp. 101–136.
   Web of Science ®Google Scholar
• Visbal, M. , and Gaitonde, D. , 2002. On the use of higher-order finite-difference schemes on curvilinear and deforming mashes , J. Comput. Phys. 181 (2002), pp. 155–185.
   Web of Science ®Google Scholar
• Xie, P. , Oliveira, M. , Su, J. , and Liu, C. , 2008. High-order weighted compact schemes for shock/boundary layer interaction , AIAA-2008-0754 (2008), Reno, NV.
   Google Scholar
• Zhou, Q. , Yao, Z. , He, F. , and Shen, M. Y. , A new family of high-order compact upwind difference schemes with good spectral resolution , J. Comput. Phys. 227, pp. 1306–1339.
   Web of Science ®Google Scholar