A new ninth‐order central Hermite weighted essentially nonoscillatory scheme for hyperbolic conservation laws

Abstract In this article, we propose a new ninth‐order central Hermite weighted essentially nonoscillatory (HWENO) scheme, for solving hyperbolic conservation laws. The new scheme consists of the following: ninth‐order reconstruction using only five points stencil; to calculate the linear weights we used the central WENO (CWENO) technique and for nonlinear weights we used a new weighting technique. The numerical solution is advanced in time by using the ninth‐order linear strong‐stability‐preserving Runge–Kutta ( ℓ SSPRK ) scheme and for computing the numerical flux, we used the central‐upwind flux which is efficient, simple and can be used for nonconex fluxes problems. The resulting scheme is ninth order in both smooth regions and at critical points with very small numerical dissipation near discontinuities, this is due to using new smoothness indicators. Several numerical examples are presented for one‐ and two‐dimensional problems to confirm that the new scheme is superior to the other high‐order WENO schemes.