An improved sixth-order WENO-type scheme by constructing new nonlinear weights for 1D/2D/3D compressible/turbulent flows

In this paper, an improved sixth-order central-upwind WENO-type scheme is proposed for solving hyperbolic conservative equations, and it is further used to simulate compressible/turbulent discontinuous flows. The improved WENO scheme, denoted I-WENO6-S, is motivated by two modifications to the existing sixth-order WENO scheme (WENO6-S), in which a new Z-type global smoothness indicator form is adopted to deduce new nonlinear weights and a modified approximation polynomial is introduced to reconstruct stencils. Meanwhile, the above same modified ideas are also embedded in another sixth-order WENO scheme (termed as “I-WENO-Z6”) for comparisons. In numerical verifications, the spectral properties of the proposed I-WENO6-S and I-WENO-Z6 schemes are first illustrated by the approximate dispersion relation (ADR), and compared with other WENO-type schemes, which indicate that the two proposed improved schemes have superior ADR to other existing schemes. Secondly, numerical errors and convergence of the proposed improved schemes are demonstrated by smoothing problems, which present that the proposed I-WENO6-S has smaller errors than other schemes under coarse mesh points. Finally, several 1D/2D/3D classical or challenging compressible discontinuous problems are simulated by the proposed improved reconstruction schemes, and compared with reference solutions, which accompanied with multi-wave, scroll-structure, implosion and small-scale isotropic turbulent vortex structures. All the numerical experiments show that the proposed I-WENO6-S is accurate and robust to predict discontinuous problems, and it has lower dispersion and dissipation than other existing sixth-order WENO-type schemes.