A New Sixth-Order WENO Scheme for Solving Hyperbolic Conservation Laws

Kunlei Zhao1,2, Yihong Du3, Yuan Li2,1
1School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China
2State Key Laboratory of Scientific and Engineering Computing (LSEC) and Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China
3School of Mathematical Sciences, Beihang University, Beijing, China

Tóm tắt

Từ khóa


Tài liệu tham khảo

Acker, F., Borges, R., Costa, B.: An improved WENO-Z scheme. J. Comput. Phys. 313, 726–753 (2016)

Balsara, D.S., Garain, S.K., Shu, C.-W.: An efficient class of WENO schemes with adaptive order. J. Comput. Phys. 326, 780–804 (2016)

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

Castro, M., Costa, B., Don, W.S.: High order weighted essentially non-oscillatory WENO-Z schemes for hyperbolic conservation laws. J. Comput. Phys. 230, 1766–1792 (2011)

Donat, R., Marquina, A.: Capturing shock reflections: an improved flux formula. J. Comput. Phys. 125, 42–58 (1996)

Fardipour, K., Mansour, K.: A modified seventh-order WENO scheme with new nonlinear weights for hyperbolic conservation laws. Comput. Math. Appl. 78, 3748–3769 (2019)

Feng, H., Hu, F.X., Wang, R.: A new mapped weighted essentially non-oscillatory scheme. J. Sci. Comput. 51, 449–473 (2012)

Feng, H., Huang, C., Wang, R.: An improved mapped weighted essentially non-oscillatory scheme. Appl. Math. Comput. 232, 453–468 (2014)

Henrick, A.K., Aslam, T.D., Powers, J.M.: Mapped weighted essentially non-oscillatory schemes: achieving optimal order near critical points. J. Comput. Phys. 207, 542–567 (2007)

Hu, F.X.: The 6th-order weighted ENO schemes for hyperbolic conservation laws. Comput. Fluids 174, 34–45 (2018)

Hu, X.Y., Wang, Q., Adams, N.A.: An adaptive central-upwind weighted essentially non-oscillatory scheme. J. Comput. Phys. 229, 8952–8965 (2010)

Huang, C., Chen, L.L.: A new adaptively central-upwind sixth-order WENO scheme. J. Comput. Phys. 357, 1–15 (2018)

Jiang, G.S., Shu, C.-W.: Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126, 202–228 (1996)

Jiang, G.S., Wu, C.C.: A high-order WENO finite difference scheme for the equations of ideal magnetohydrodynamics. J. Comput. Phys. 150, 561–594 (1999)

Lax, P.D.: Weak solutions of nonlinear hyperbolic equations and their numerical computation. Commun. Pure Appl. Math. 7, 159–193 (1954)

Levy, D., Puppo, G., Russo, G.: Central WENO schemes for hyperbolic systems of conservation laws. Math. Model. Numer. Anal. 33, 547–571 (1999)

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

Martin, M.P., Taylor, E.M., Wu, M., Weirs, V.G.: A bandwidth-optimized WENO scheme for the effective direct numerical simulation of compressible turbulence. J. Comput. Phys. 220, 270–289 (2006)

Nonomura, T., Kitamura, K., Fujii, K.: A simple interface sharpening technique with a hyperbolic tangent function applied to compressible two-fluid modeling. J. Comput. Phys. 258, 95–117 (2014)

Peng, J., Zhai, C.L., Ni, G.X., Yong, H., Shen, Y.Q.: An adaptive characteristic-wise reconstruction WENO-Z scheme for gas dynamic Euler equations. Comput. Fluids 179, 34–51 (2019)

Schulz-Rinne, C.-W., Collins, J.P., Glaz, H.M.: Numerical solution of the Riemann problem for two-dimensional gas dynamics. SIAM J. Sci. Comput. 14, 1394–1414 (1993)

Shu, C.-W.: Total-variation-diminishing time discretizations. SIAM J. Sci. Stat. Comput. 9, 1073–1084 (1988)

Shu, C.-W., Osher, S.: Efficient implement of essentially non-oscillatory shock capturing schemes. II. J. Comput. Phys. 83, 32–78 (1989)

Sod, G.A.: A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws. J. Comput. Phys. 27, 1–31 (1978)

Sun, Z.Y., Inaba, S., Xiao, F.: Boundary variation diminishing (BVD) reconstruction: a new approach to improve Godunov schemes. J. Comput. Phys. 322, 309–325 (2016)

Toro, E.F.: Riemann Solvers and Numerical Methods for Fluid Dynamics, pp. 87–114. Springer, Berlin (2013)

Wang, Y.H., Du, Y.L., Zhao, K.L., Yuan, L.: A new 6th-order WENO scheme with modified stencils. Comput. Fluids 208, 104625 (2020)

Woodward, P.R., Colella, P.: The numerical simulation of two-dimensional fluid flow with strong shocks. J. Comput. Phys. 54, 115–173 (1984)

Zhu, J., Qiu, J.X.: A new fifth order finite difference WENO scheme for solving hyperbolic conservation laws. J. Comput. Phys. 318, 110–121 (2016)