1. van Albada, G.D., van Leer, B., Roberts, W.W., Jr.: A comparative study of computational methods in cosmic gas dynamics. Astron. Astrophys. 108(1), 76–84 (1982)
2. Arminjon, P., St-Cyr, A., Madrane, A.: New two- and three-dimensional non-oscillatory central finite volume methods on staggered Cartesian grids. Appl. Numer. Math. 40(3), 367–390 (2002)
3. Balbás, J., Tadmor, E.: Central station—a collection of references on high-resolution non-oscillatory central schemes (2006). https:// www. math. umd. edu/ ~tadmor/ centp ack/ publi catio ns/
4. Balbás, J., Tadmor, E., Wu, C.-C.: Non-oscillatory central schemes for one- and two-dimensional MHD equations: I. J. Comput. Phys. 201(1), 261–285 (2004)
5. Chakravarthy, S., Osher, S.: A new class of high accuracy TVD schemes for hyperbolic conservation laws. In: 23rd Aerospace Sciences Meeting, p. 363 (1985)
6. Einfeldt, B.: On Godunov-type methods for gas dynamics. SIAM J. Numer. Anal. 25(2), 294–318 (1988)
7. Engquist, B., Osher, S.: One-sided difference approximations for nonlinear conservation laws. Math. Comput. 36(154), 321–351 (1981)
8. Fjordholm, U.S., Mishra, S., Tadmor, E.: Arbitrarily high-order accurate entropy stable essentially nonoscillatory schemes for systems of conservation laws. SIAM J. Numer. Anal. 50(2), 544–573 (2012)
9. Fjordholm, U.S., Mishra, S., Tadmor, E.: ENO reconstruction and ENO interpolation are stable. Found. Comput. Math. 13, 139–159 (2013)
10. Fjordholm, U.S., Ray, D.: A sign preserving WENO reconstruction method. J. Sci. Comput. 68, 42–63 (2016)
11. Godunov, S.K.: A finite difference method for the numerical computation of discontinuous solutions of the equations of fluid dynamics. Mat. Sb. 47, 357–393 (1959)
12. Gottlieb, S., Ketcheson, D.I., Shu, C.-W.: Strong Stability Preserving Runge-Kutta and Multistep Time Discretizations. World Scientific, Singapore (2011)
13. Gottlieb, S., Shu, C.-W., Tadmor, E.: Strong stability-preserving high-order time discretization methods. SIAM Rev. 43(1), 89–112 (2001)
14. Harten, A.: High resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 135(2), 260– 278 (1997)
15. Harten, A., Engquist, B., Osher, S., Chakravarthy, S.R.: Uniformly high order accurate essentially nonoscillatory schemes, III. J. Comput. Phys. 71(2), 231–303 (1987)
16. Harten, A., Hyman, J.M., Lax, P.D., Keyfitz, B.: On finite-difference approximations and entropy conditions for shocks. Commun. Pure Appl. Math. 29(3), 297–322 (1976)
17. Harten, A., Lax, P.D., van Leer, B.: On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Rev. 25(1), 35–61 (1983)
18. Harten, A., Osher, S.: Uniformly high-order accurate nonoscillatory schemes. I. In: Upwind and HighResolution Schemes, pp. 187–217. Springer, Berlin (1997)
19. Jiang, G.-S., Tadmor, E.: Nonoscillatory central schemes for multidimensional hyperbolic conservation laws. SIAM J. Sci. Comput. 19(6), 1892–1917 (1998)
20. Johnson, C., Szepessy, A., Hansbo, P.: On the convergence of shock-capturing streamline diffusion finite element methods for hyperbolic conservation laws. Math. Comput. 54(189), 107–129 (1990)
21. Kupferman, R., Tadmor, E.: A fast, high resolution, second-order central scheme for incompressible flows. Proc. Natl. Acad. Sci. 94(10), 4848–4852 (1997)
22. Kurganov, A., Levy, D.: A third-order semidiscrete central scheme for conservation laws and convection-diffusion equations. SIAM J. Sci. Comput. 22(4), 1461–1488 (2000)
23. Kurganov, A., Noelle, S., Petrova, G.: Semidiscrete central-upwind schemes for hyperbolic conservation laws and Hamilton-Jacobi equations. SIAM J. Sci. Comput. 23(3), 707–740 (2001)
24. Kurganov, A., Tadmor, E.: New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations. J. Comput. Phys. 160(1), 241–282 (2000)
25. Lax, P.D.: Weak solutions of nonlinear hyperbolic equations and their numerical computation. Commun. Pure Appl. Math. 7, 159–193 (1954)
26. van Leer, B.: Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method. J. Comput. Phys. 32(1), 101–136 (1979)
27. van Leer, B.: On the relation between the upwind-differencing schemes of Godunov, EngquistOsher and Roe. SIAM J. Sci. Stat. Comput. 5(1), 1–20 (1984)
28. Levy, D., Puppo, G., Russo, G.: Central WENO schemes for hyperbolic systems of conservation laws. ESAIM Math. Model. Numer. Anal. 33(3), 547–571 (1999)
29. Levy, D., Puppo, G., Russo, G.: A third order central WENO scheme for 2D conservation laws. Appl. Numer. Math. 33(1/2/3/4), 415–421 (2000)
30. Levy, D., Puppo, G., Russo, G.: A fourth-order central WENO scheme for multidimensional hyperbolic systems of conservation laws. SIAM J. Sci. Comput. 24(2), 480–506 (2002)
31. Levy, D., Tadmor, E.: Non-oscillatory central schemes for the incompressible 2-D Euler equations. Math. Res. Lett. 4(3), 321–340 (1997)
32. Liu, X.-D., Osher, S., Chan, T.: Weighted essentially non-oscillatory schemes. J. Comput. Phys. 115(1), 200–212 (1994)
33. Liu, X.-D., Tadmor, E.: Third order nonoscillatory central scheme for hyperbolic conservation laws. Numer. Math. 79(3), 397–425 (1998)
34. Liu, Y., Shu, C.-W., Tadmor, E., Zhang, M.: L2 stability analysis of the central discontinuous Galerkin method and a comparison between the central and regular discontinuous Galerkin methods. ESAIM Math. Model. Numer. Anal. 42(4), 593–607 (2008)
35. Mulder, W.A., van Leer, B.: Experiments with implicit upwind methods for the Euler equations. J. Comput. Phys. 59(2), 232–246 (1985)
36. Nessyahu, H., Tadmor, E.: Non-oscillatory central differencing for hyperbolic conservation laws. J. Comput. Phys. 87(2), 408–463 (1990)
37. Osher, S.: Riemann solvers, the entropy condition, and difference. SIAM J. Numer. Anal. 21(2), 217–235 (1984)
38. Osher, S.: Convergence of generalized MUSCL schemes. SIAM J. Numer. Anal. 22(5), 947–961 (1985)
39. Osher, S., Tadmor, E.: On the convergence of difference approximations to scalar conservation laws. Math. Comput. 50(181), 19–51 (1988)
40. Piperno, S., Depeyre, S.: Criteria for the design of limiters yielding efficient high resolution TVD schemes. Comput. Fluids 27(2), 183–197 (1998)
41. Roe, P.L.: Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 43(2), 357–372 (1981)
42. Saurel, R., Abgrall, R.: A simple method for compressible multifluid flows. SIAM J. Sci. Comput. 21(3), 1115–1145 (1999)
43. Shu, C.-W.: TVB uniformly high-order schemes for conservation laws. Math. Comput. 49(179), 105–121 (1987)
44. Shu, C.-W.: Total-variation-diminishing time discretizations. SIAM J. Sci. Stat. Comput. 9(6), 1073–1084 (1988)
45. Shu, C.-W.: Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. In: Cockburn, B., Shu, C.-W., Johnson, C., Tadmor, E. (eds.) Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, pp. 285–372. Springer, Berlin (1998)
46. Shu, C.-W.: Essentially non-oscillatory and weighted essentially non-oscillatory schemes. Acta Numer. 29, 701–762 (2020)
47. Shur, M.L., Spalart, P.R., Strelets, M.K.: Noise prediction for increasingly complex jets. Part I: methods and tests. Int. J. Aeroacoust. 4(3), 213–245 (2005)
48. Spiteri, R.J., Ruuth, S.J.: A new class of optimal high-order strong-stability-preserving time discretization methods. SIAM J. Numer. Anal. 40(2), 469–491 (2002)
49. Sweby, P.K.: High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM J. Numer. Anal. 21(5), 995–1011 (1984)
50. Tadmor, E.: Numerical viscosity and the entropy condition for conservative difference schemes. Math. Comput. 43(168), 369–381 (1984)
51. Tadmor, E.: Convenient total variation diminishing conditions for nonlinear difference schemes. SIAM J. Numer. Anal. 25(5), 1002–1014 (1988)
52. Tadmor, E.: Total variation and error estimates for spectral viscosity approximations. Math. Comput. 60(201), 245–256 (1993)
53. Tadmor, E.: Approximate solutions of nonlinear conservation laws and related equations. In: Cockburn, B., Shu, C.-W., Johnson, C., Tadmor, E. (eds.) Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, pp. 1–149. Springer, Berlin (1998)
54. Tadmor, E.: Entropy stability theory for difference approximations of nonlinear conservation laws and related time-dependent problems. Acta Numer. 12, 451–512 (2003)
55. Tadmor, E.: Selected topics in approximate solutions of nonlinear conservation laws. High-resolution central schemes. In: Nonlinear Conservation Laws and Applications, pp. 101–122. Springer, New York (2011)
56. Toro, E.F., Spruce, M., Speares, W.: Restoration of the contact surface in the HLL-Riemann solver. Shock Waves 4(1), 25–34 (1994)
57. Wang, S., Xu, Z.: Total variation bounded flux limiters for high order finite difference schemes solving one-dimensional scalar conservation laws. Math. Comput. 88(316), 691–716 (2019)
58. Woodward, P., Colella, P.: The numerical simulation of two-dimensional fluid flow with strong shocks. J. Comput. Phys. 54(1), 115–173 (1984)
59. Zenginoglu, A.: Centpy: central schemes for conservation laws in python (2020). https:// pypi. org/ proje ct/ centpy/
60. Zhang, J., Jackson, T.L.: A high-order incompressible flow solver with WENO. J. Comput. Phys. 228(7), 2426–2442 (2009)
