WENO schemes: a list of schemes to be implemented

[szaghi]

Just a list of schemes that we would like to be implemented into the library:

• [x] Efficient Implementation of Weighted ENO Schemes, Guang-Shan Jiang, Chi-Wang Shu, JCP, 1996, vol. 126, pp. 202--228, doi:10.1006/jcph.1996.0130
  • [x] formal 3rd order, S=2;
  • [x] formal 5th order, S=3;
  • [x] formal 7th order, S=4, from Balsara et al.¹;
  • [x] formal 9th order, S=5, from Balsara et al.¹;
  • [x] formal 11th order, S=6, from Balsara et al.¹;
  • [x] formal 13th order, S=7, from Gerolyms et al.²;
  • [x] formal 15th order, S=8, from Gerolyms et al.²;
  • [x] formal 17th order, S=9, from Gerolyms et al.²;
• [x] Weno Interpolation, from High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems, Chi-Wang Shu, SIAM Review, 2009, vol. 51, pp. 82--126, doi:10.1137/070679065
  • [x] formal 3rd order, S=2;
  • [x] formal 5th order, S=3;
  • [x] formal 7th order, S=4;
  • [x] formal 9th order, S=5;
  • [x] formal 11th order, S=6;
  • [x] formal 13th order, S=7;
  • [x] formal 15th order, S=8;
  • [x] formal 17th order, S=9;
• [ ] A bandwidth-optimized WENO scheme for the effective direct numerical simulation of compressible turbulence, M.P. Martín, E.M. Taylor, M. Wu, V.G. Weirs, JCP, 2006, vol. 220, pp. 270--289, doi:10.1016/j.jcp.2006.05.009
• [x] An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws, Rafael Borges, Monique Carmona, Bruno Costa, Wai Sun Don, JCP, 2007, vol. 227, pp. 3191--3211, doi:10.1016/j.jcp.2007.11.038
• [ ] Weights Design For Maximal Order WENO Schemes, F. Aràndiga, P. Mulet, JSC, 2014, vol. 60, pp. 641-659, doi:10.1007/s10915-013-9810-0
• [ ] Compact Reconstruction Schemes with Weighted ENO Limiting for Hyperbolic Conservation Laws, D. Ghosh, J. D. Baeder, JSC, 2012, vol. 34, pp. 1678-1706, doi:10.1137/110857659
• [ ] A new class of central compact schemes with spectral-like resolution II: Hybrid weighted nonlinear schemes, Xuliang Liu, Shuhai Zhang, Hanxin Zhang, Chi-Wang Shu, JCP, 2015, vol. 284, pp. 133-154, doi:10.1016/j.jcp.2014.12.027

[1] Monotonicity Preserving Weighted Essentially Non-oscillatory Schemes with Increasingly High Order of Accuracy, Dinshaw S. Balsara and Chi-Wang Shu, JCP, vol. 160, n. 2, 2000, pp. 405-452 [2] Very-high-order WENO Sceheme, G.A. Gerolymos, D. Sénéchal, I. Vallet, JPC, vol. 228, n. 23, 2009, pp. 8481-8524