[1] LIU X D, OSHER S, CHAN T. Weighted essentially non-oscillatory schemes[J]. Journal of Computational Physics, 1994, 115(1): 200-212. [2] HARTEN A, ENGQUIST B, OSHER S, et al. Uniformly high order accurate essentially non-oscillatory schemes, III[J]. Journal of Computational Physics, 1987, 71(1):231-303. [3] JIANG G S, SHU C W. Efficient implementation of weighted ENO schemes[J]. Journal of Computational Physics, 1996, 126(1): 202-228. [4] WANG Z J, CHEN R F. Optimized weighted essentially non-oscillatory schemes for linear waves with discontinuity[J]. Journal of Computational Physics, 2001, 174(1): 381-404. [5] HENRICK A K, ASLAM T D, POWERS J M. Mapped weighted essentially non-oscillatory schemes: Achieving optimal order near critical points[J]. Journal of Computational Physics, 2005, 207(2): 542-567. [6] MARTÍN M P, TAYLOR E M, WU M, et al. A bandwidth-optimized WENO scheme for the effective direct numerical simulation of compressible turbulence[J]. Journal of Computational Physics, 2006, 220(1): 270-289. [7] BORGES R, CARMONA M, COSTA B, et al. An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws[J]. Journal of Computational Physics, 2008, 227(6): 3191-3211. [8] SHEN Y Q, ZHA G C. Improvement of weighted essentially non-oscillatory schemes near discontinuities[J]. Computers & Fluids, 2014, 96: 1-9. [9] MA Y K, YAN Z G, ZHU H J. Improvement of multistep WENO scheme and its extension to higher orders of accuracy[J]. International Journal for Numerical Methods in Fluids, 2016, 82(12): 818-838. [10] HONG Z, YE Z Y, MENG X Z. A mapping-function-free WENO-M scheme with low computational cost[J]. Journal of Computational Physics, 2020, 405: 109145. [11] SURESH A, HUYNH H T. Accurate monotonicity-preserving schemes with Runge-Kutta time stepping[J]. Journal of Computational Physics, 1997, 136(1): 83-99. [12] BALSARA D S, SHU C W. Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy[J]. Journal of Computational Physics, 2000, 160(2): 405-452. [13] FU D X, MA Y W. Analysis of super compact finite difference method and application to simulation of vortex-shock interaction[J]. International Journal for Numerical Methods in Fluids, 2001, 36(7): 773-805. [14] ADAMS N A, SHARIFF K. A high-resolution hybrid compact-ENO scheme for shock-turbulence interaction problems[J]. Journal of Computational Physics, 1996, 127(1): 27-51. [15] COCKBURN B, SHU C W. The Runge-Kutta discontinuous Galerkin method for conservation laws V: multidimensional systems[J]. Journal of Computational Physics, 1998, 141(2): 199-224. [16] QIU J X, SHU C W. Runge-Kutta discontinuous Galerkin method using WENO limiters[J]. SIAM Journal on Scientific Computing, 2005, 26(3): 907-929. [17] XU K, PRENDERGAST K H. Numerical Navier-Stokes solutions from gas kinetic theory[J]. Journal of Computational Physics, 1994, 114(1): 9-17. [18] XU K. Gas-kinetic schemes for unsteady compressible flow simulations[C]//29th Computational Fluid Dynamics, Annual Lecture Series, 1998. [19] XU K. A gas-kinetic BGK scheme for the Navier-Stokes equations and its connection with artificial dissipation and Godunov method[J]. Journal of Computational Physics, 2001, 171(1): 289-335. [20] DESHPANDE S. Kinetic theory based new upwind methods for inviscid compressible flows[C]//24th Aerospace Sciences Meeting, 1986. [21] PULLIN D I. Direct simulation methods for compressible inviscid ideal-gas flow[J]. Journal of Computational Physics, 1980, 34(2): 231-244. [22] MANDAL J C, DESHPANDE S M. Kinetic flux vector splitting for Euler equations[J]. Computers & Fluids, 1994, 23(2): 447-478. [23] CHOU S Y, BAGANOFF D. Kinetic flux-vector splitting for the Navier-Stokes equations[J]. Journal of Computational Physics, 1997, 130(2): 217-230. [24] CHEN Y B, JIANG S. Modified kinetic flux vector splitting schemes for compressible flows[J]. Journal of Computational Physics, 2009, 228(10): 3582-3604. [25] XIONG S W, ZHONG C W, ZHUO C S, et al. Numerical simulation of compressible turbulent flow via improved gas-kinetic BGK scheme[J]. International Journal for Numerical Methods in Fluids, 2011, 67(12): 1833-1847. [26] LIAO W, PENG Y, LUO L S. Gas-kinetic schemes for direct numerical simulations of compressible homogeneous turbulence[J]. Physical Review E, 2009, 80(4): 046702. [27] SUN Z S, REN Y X, LARRICQ C, et al. A class of finite difference schemes with low dispersion and controllable dissipation for DNS of compressible turbulence[J]. Journal of Computational Physics, 2011, 230(12): 4616-4635. [28] HE Z W, LI X L, LIANG X. Nonlinear spectral-like schemes for hybrid schemes[J]. Science China Physics, Mechanics and Astronomy, 2014, 57(4): 753-763. [29] LIU H W. A hybrid kinetic WENO scheme for inviscid and viscous flows[J]. International Journal for Numerical Methods in Fluids, 2015, 79(6): 290-305. [30] COCKBURN B, SHU C W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. II. General framework[J]. Mathematics of Computation, 1989, 52(186): 411-435. [31] KRIVODONOVA L, XIN J, REMACLE J F, et al. Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws[J]. Applied Numerical Mathematics, 2004, 48(3-4): 323-338. [32] XU Z F, SHU C W. Anti-diffusive flux corrections for high order finite difference WENO schemes[J]. Journal of Computational Physics, 2005, 205(2): 458-485. [33] SURESH A, HUYNH H T. Accurate monotonicity-preserving schemes with Runge-Kutta time stepping[J]. Journal of Computational Physics, 1997, 136(1): 83-99. [34] HARTEN A. Adaptive multiresolution schemes for shock computations[J]. Journal of Computational Physics, 1994, 115(2): 319-338. [35] LI G, QIU J X. Hybrid weighted essentially non-oscillatory schemes with different indicators[J]. Journal of Computational Physics, 2010, 229(21): 8105-8129. [36] RAY D, HESTHAVEN J S. An artificial neural network as a troubled-cell indicator[J]. Journal of Computational Physics, 2018, 367: 166-191. [37] RAY D, HESTHAVEN J S. Detecting troubled-cells on two-dimensional unstructured grids using a neural network[J]. Journal of Computational Physics, 2019, 397: 108845. [38] ABGRALL R, HAN VEIGA M. Neural network-based limiter with transfer learning[J]. Communications on Applied Mathematics and Computation, 2020: 1-41. [39] SUN Z. Convolution neural network shock detector for numerical solution of conservation laws[J]. Communications in Computational Physics, 2020, 28(5): 2075-2108. [40] SHU C W, OSHER S. Efficient implementation of essentially non-oscillatory shock-capturing schemes[J]. Journal of Computational Physics, 1988, 77(2): 439-471. [41] STEGER J L, WARMING R F. Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods[J]. Journal of Computational Physics, 1981, 40(2): 263-293. [42] OHWADA T, FUKATA S. Simple derivation of high-resolution schemes for compressible flows by kinetic approach[J]. Journal of Computational Physics, 2006, 211(2): 424-447. [43] GUO Z L, LIU H W, LUO L S, et al. A comparative study of the LBE and GKS methods for 2D near incompressible laminar flows[J]. Journal of Computational Physics, 2008, 227(10): 4955-4976. [44] TITAREV V A, TORO E F. Finite-volume WENO schemes for three-dimensional conservation laws[J]. Journal of Computational Physics, 2004, 201(1): 238-260. [45] SCHULZ-RINNE C W, COLLINS J P, GLAZ H M. Numerical solution of the Riemann problem for two-dimensional gas dynamics[J]. SIAM Journal on Scientific Computing, 1993, 14(6): 1394-1414. [46] WOODWARD P, COLELLA P. The numerical simulation of two-dimensional fluid flow with strong shocks[J]. Journal of Computational Physics, 1984, 54(1): 115-173. |