[1] HARTEN, A., ENGQUIST, B., OSHER, S., and CHAKRAVARTHY, S. R. Uniformly high order accurate essentially non-oscillatory schemes, III. Journal of Computational Physics, 71, 231-303(1987)
[2] HU, C. and SHU, C. W. Weighted essentially non-oscillatory schemes on triangular meshes. Journal of Computational Physics, 150, 97-127(1999)
[3] REED, W. H. and HILL, T. R. Triangular mesh methods for the neutron transport equation. Technical Report LA-UR-73-479, Los Alamos Scientif Laboratory (1973)
[4] KOPRIVA, D. A. and KOLIAS, J. H. A conservative staggered-grid Chebyshev multidomain method for compressible flows. Journal of Computational Physics, 125, 244-261(1996)
[5] HUYNH, H. T. A flux reconstruction approach to high-order schemes including discontinuous Galerkin methods. 18th AIAA Computational Fluid Dynamics Conference, 2007-4079(2007)
[6] HESTHAVEN, J. S. and WARBURTON, T. Nodal Discontinuous Galerkin Methods, Springer (2008)
[7] WANG, Z. J. and GAO, H. A unifying lifting collocation penalty formulation including the discontinuous Galerkin, spectral volume/difference methods for conservation laws on mixed grids. Journal of Computational Physics, 228, 8161-8186(2009)
[8] YU, M., WANG, Z. J., and LIU, Y. On the accuracy and efficiency of discontinuous Galerkin, spectral difference and correction procedure via reconstruction methods. Journal of Computational Physics, 259, 70-95(2014)
[9] JAMESON, A., VINCENT, P. E., and CASTONGUAY, P. On the non-linear stability of flux reconstruction schemes. Journal of Scientific Computing, 50, 434-445(2012)
[10] VINCENT, P. E., CASTONGUAY, P., and JAMESON, A. A new class of high-order energy stable flux reconstruction schemes. Journal of Scientific Computing, 47, 50-72(2011)
[11] ROE, P. L. Approximate Riemann solvers, parameter vectors, and difference schemes. Journal of Computational Physics, 43, 357-372(1981)
[12] LIOU, M. S. and STEFFEN, C. J. A new flux splitting scheme. Journal of Computational Physics, 107, 23-39(1993)
[13] HARTEN, A., LAX, P. D., and VAN LEER, B. On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Review, 25, 35-61(1983)
[14] KITAMURA, K., SHIMA, E., and ROE, P. L. Evaluation of Euler fluxes for hypersonic heating computations. AIAA Journal, 48, 763-776(2010)
[15] ALEXANDER, F. J., CHEN, S., and STERLING, J. Lattice Boltzmann thermos hydrodynamics. Physical Review E, 47, 2249(1993)
[16] SHI, W., SHYY, W., and MEI, R. Finite-difference-based lattice Boltzmann method for inviscid compressible flows. Numerical Heat Transfer, Part B:Fundamentals, 40, 1-21(2001)
[17] KATAOKA, T. and TSUTAHARA, M. Lattice Boltzmann method for the compressible Euler equations. Physical Review E, 69, 056702(2004)
[18] JI, C. Z., SHU, C., and ZHAO, N. A lattice Boltzmann method-based flux solver and its application to solver shock tube problem. Modern Physics Letters B, 23, 313-316(2009)
[19] YANG, L. M., SHU, C., and WU, J. Development and comparative studies of three non-free parameter lattice Boltzmann models for simulation of compressible flows. Advances in Applied Mathematics and Mechanics, 4, 454-472(2012)
[20] YANG, L. M., SHU, C., and WU, J. A moment conservation-based non-free parameter compressible lattice Boltzmann model and its application for flux evaluation at cell interface. Computers and Fluids, 79, 190-199(2013)
[21] YANG, L. M., SHU, C., and WU, J. A hybrid lattice Boltzmann flux solver for simulation of viscous compressible flows. Advances in Applied Mathematics and Mechanics, 8, 887-910(2016)
[22] XU, K. A gas-kinetic BGK scheme for the Navier-Stokes equations and its connection with artificial dissipation and Godunov method. Journal of Computational Physics, 171, 289-335(2001)
[23] XU, K. Regularization of the Chapman-Enskog expansion and its description of shock structure. Physics of Fluids, 14, 17-20(2002)
[24] GUO, Z. L. and SHU, C. Lattice Boltzmann Method and its Applications in Engineering, World Scientific Publishing, 365-404(2013)
[25] COCKBURN, B. and SHU, C. W. The local discontinuous Galerkin method for time-dependent convection-diffusion systems. SIAM Journal on Numerical Analysis, 35, 2440-2463(1998)
[26] WITHERDEN, F. D., FARRINGTON, A. M., and VINCENT, P. E. PyFR:an open source framework for solving advection-diffusion type problems on streaming architectures using the flux reconstruction approach. Computer Physics Communications, 185, 3028-3040(2014)
[27] PERSSON, P. O. and PERAIRE, J. Sub-cell shock capturing for discontinuous Galerkin methods. 44th AIAA Aerospace Sciences Meeting and Exhibit, American Institute of Aeronautics and Astronautics, 2006-112(2006)
[28] LASKOWSKI W., RUEDA-RAMIREZ, A. M., RUBIO, G., VALERO, E., and FERRER, E. Advantages of static condensation in implicit compressible Navier-Stokes DGSEM solvers. Computers and Fluids, 209, 104646(2020)
[29] GHIA, U., GHIA, K. N., and SHIN, C. T. High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. Journal of Computational Physics, 48, 387-411(1982)
[30] ERTURK, E., CORKE, T. C., and GOKCOL, C. Numerical solutions of 2-D steady incompressible driven cavity flow at high Reynolds numbers. International Journal for Numerical Methods in Fluids, 48, 747-774(2005)
[31] TAKAHASHI, S., NONOMURA, T., and FUKUDA, K. A numerical scheme based on an immersed boundary method for compressible turbulent flows with shocks applications to two-dimensional flows around cylinders. Journal of Applied Mathematics, 10, 1155-1175(2014)
[32] BHARADWAJ, A. and GHOSH, S. Data reconstruction at surface in immersed-boundary methods. Computers & Fluids, 196, 104236(2019)
[33] JAWAHAR, P. and KAMATH, H. A high-resolution procedure for Euler and Navier-Stokes computations on unstructured grids. Journal of Computational Physics, 164, 165-203(2000)
[34] BRISTEAU, M. O., GLOWINSKI, R., PERIAUX, J., and VIANDVIAND, H. Numerical Simulation of Compressible Navier-Stokes Flows, John Wiley, London (1987)
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