[1]
Borges, R., Carmona, M., Costa, B. and Don, W. S., An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws, J. Comput. Phys., 227 (2008), pp. 3191–3211.

[2]
Acker, F., De R. Borges, R. B. and Costa, B., An improved WENO-Z scheme, J. Comput. Phys., 313 (2016), pp. 726–753.

[3]
Ben-Artzi, M., Falcovitz, J., A second-order Godunov-type scheme for compressible uid dynamics, J. Comput. Phys., 55 (1984), pp. 1–32.

[4]
Ben-Artzi, M., Li, J. and Warnecke, G., A direct Eulerian GRP scheme for compressible fluid flows, J. Comput. Phys., 218 (2006), pp. 19–43.

[5]
Ben-Artzi, M. and Li, J., Hyperbolic conservation laws: Riemann invariants and the generalized Riemann problem, Numerische Mathematik, 106 (2007), pp. 369–425.

[6]
Bhatnagar, P. L., Gross, E. P. and Krook, M., A Model for Collision Processes in Gases I: Small Amplitude Processes in Charged and Neutral One-Component Systems, Phys. Rev., 94 (1954), pp. 511–525.

[7]
Boris, J. P., A fluid transport algorithm that works, in: Computing as a Language of Physics, International Atomic Energy Commision, (1971), pp. 171–189.

[8]
Chapman, S. and Cowling, T. G., The Mathematical Theory of Non-Uniform Gases, 3rd ed, Cambridge University Press, (1990).

[9]
Christlieb, A. J., Gottlieb, S., Grant, Z. and Seal, D. C., Explicit strong stability preserving multistage two-derivative time-stepping scheme, J. Sci. Comp., 68 (2016), pp. 914–942.

[10]
Cockburn, B. and Shu, C. W., TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: general framework, Math. Comput., 52 (1989), pp. 411–435.

[11]
Courant, R. and Friedrichs, K. O., Supersonic Flow and Shock Waves, Springer, (1948).

[12]
Cockburn, B. and Shu, C. W., The Runge-Kutta discontinuous Galerkin method for conservation laws V: multidimensional systems, J. Comput. Phys., 141 (1998), pp. 199–224.

[13]
Harten, A., High resolution schemes for hyperbolic conservation laws, J. Comput. Phys., 49 (1983), pp. 357–393.

[14]
Han, E., Li, J. and Tang, H., Accuracy of the adaptive GRP scheme and the simulation of 2-D Riemann problem for compressible Euler equations, Comm. Comput. Phys., 10 (2011), pp. 577–606.

[15]
Glimm, J., Ji, X., Li, J., Li, X., Zhang, P., Zhang, T. and Zheng, Y., Transonic shock formation in a rarefaction Riemann problem for the 2D compressible Euler equations, SIAM J. Appl. Math., 69 (2008), pp. 720–742.

[16]
Harten, A., Engquist, B., Osher, S. and Chakravarthy, S. R., Uniformly high order accurate essentially non-oscillatory schemes, III. J. Comput. Phys., 71 (1987), pp. 231–303.

[17]
Jiang, G. S. and Shu, C. W., Efficient implementation of Weighted ENO schemes, J. Comput. Phys., 126 (1996), pp 202–228.

[18]
Kolgan, V. P., Application of the principle of minimum values of the derivative to the construction of finite-difference schemes for calculating discontinuous solutions of gas dynamics, Scientific Notes of TsAGI, 3 (1972), pp. 68–77.

[19]
Kreiss, H. O. and Lorenz, J., Initial-Boundary Value Problems and the Navier-Stokes Equations, Academic Press, (2004).

[20]
Kurganov, A. and Tadmor, E., Solution of two-dimensional Riemann problems for gas dynamics without Riemann problem solvers, Numer. Meth. Part. Diff. Eqs., 18 (2002), pp. 584–608.

[21]
Lax, P. D. and Liu, X. D., Solution of two-dimensional Riemann problems of gas dynamics by positive schemes, SIAM J. Sci. Comput., 19 (1998), pp. 319–340.

[22]
Lax, P. and Wendroff, B., Systems of conservation laws, Comm. Pure Appl. Math., 13 (1960), pp. 217–237.

[23]
Lee, C. B., New features of CS solitons and the formation of vortices, Phys. Lett. A, 247(6) (2008), pp. 397–402.

[24]
Lee, C. B., Possible universal transitional scenario in a flat plate boundary layer: Measurement and visualization, Phys. Rev. E, 62(3) (2000), 3659.

[25]
Lee, C. B. and Wu, J. Z., Transition in wall-bounded flows, Appl. Mech. Rev., 61(3) (2008), 0802.

[26]
Li, J., Du, Z., A Two-Stage Fourth Order Time-Accurate Discretization for Lax-Wendroff Type Flow Solvers, I. Hyperbolic Conservation Laws, Mathematics, 2016.

[27]
Li, J., Zhang, T. and Yang, S., The Two-Dimensional Riemann Problem in Gas Dynamics, Addison Wesley Longman, (1998).

[28]
Li, J., Note on the compressible Euler equations with zero temperature, Appl. Math. Lett., 14 (2001), pp. 519–523.

[29]
Li, J. and Zheng, Y., Interaction of four rarefaction waves in the bi-symmetric class of the two-dimensional Euler equations, Comm. Math. Phys., 296 (2010), pp. 303–321.

[30]
Li, Q., Xu, K. and Fu, S., A high-order gas-kinetic Navier-Stokes flow solver, J. Comput. Phys., 229 (2010), pp. 6715–6731.

[31]
Liu, X. D., Osher, S. and Chan, T., Weighted essentially non-oscillatory schemes, J. Comput. Phys., 115 (1994), pp. 200–212.

[32]
Luo, J. and Xu, K., A high-order multidimensional gas-kinetic scheme for hydrodynamic equations, Science China Technological Sciences, 56 (2013), pp. 2370–2384.

[33]
Majda, A., Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables, Applied Mathematical Sciences, Springer-Verlag, New York, 53 (1984).

[34]
Pan, L., Xu, K., Li, Q. and Li, J., An efficient and accurate two-stage fourth-order gas-kinetic scheme for the Navier-Stokes equations, J. Comput. Phys.
326 (2016), pp. 197–221.

[35]
Reed, W. H. and Hill, T. R., Triangular Mesh Methods for the Neutron Transport Equation, Technical Report LA-UR-73-479, Los Alamos Scientific Laboratory, Los Alamos, 1973.

[36]
W. E, , Rykov, Y. G. and Sinai, Y. G., Generalized variational principles, global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamics, Comm. Math. Phys., 177 (1996), pp. 349–380.

[37]
Schulz-Rinne, C. W., Collins, J. P. and Glaz, H. M., Numerical solution of the Riemann problem for twodimensional gas dynamics, SIAM J. Sci. Comput., 14 (1993), pp. 1394–1414.

[38]
Seal, D. C., Güclü, Y. and Christlieb, A. J., High-order multiderivative time integrators for hyperbolic conservation laws, J. Sci. Comp., 60 (2014), pp. 101–140.

[39]
Shi, J., Zhang, Y. T. and Shu, C. W., Resolution of high order WENO schemes for complicated flow structures, J. Comput. Phys., 186 (2003), pp. 690–696.

[40]
Sheng, W. and Zhang, T., The Riemann problem for the transportation equations in gas dynamics, Mem. Amer. Math. Soc., 654(654) (1999), pp. 77.

[41]
Shu, C. W. and Osher, S., Efficient implementation of essentially non-oscillatory shock capturing schemes, J. Comput. Phys., 77 (1988), pp. 439–471.

[42]
Tang, H. Z. and Liu, T. G., A note on the conservative schemes for the Euler equations, J. Comput. Phys., 218 (2006), pp. 451–459.

[43]
Titarev, V. A. and Toro, E. F., Finite volume WENO schemes for three-dimensional conservation laws, J. Comput. Phys.
201 (2014), pp. 238–260.

[44]
Van Leer, B., Towards the ultimate conservative difference scheme. V. A second order sequel to Godunov's method, J. Comput. Phys., 32 (1979), pp. 101–136.

[45]
Woodward, P. and Colella, P., Numerical simulations of two-dimensional fluid flow with strong shocks, J. Comput. Phys., 54 (1984), pp. 115–173.

[46]
Xu, K., Direct modeling for computational fluid dynamics: construction and application of unfied gas kinetic schemes, World Scientific, (2015).

[47]
Xu, K., A gas-kinetic BGK scheme for the Navier-Stokes equations and its connection with artificial dissipation and Godunov method, J. Comput. Phys., 171 (2001), pp. 289–335.

[48]
Zhang, T. and Zheng, Y., Exact spiral solutions of the two-dimensional Euler equations, Discrete Contin. Dynam. Systems, 3 (1997), pp. 117–133.

[49]
Zhang, T. and Zheng, Y., Conjecture on the structure of solutions of the Riemann problem for two dimensional gas dynamics systems, SIAM J. Math. Anal., 21 (1990), pp. 593–630.