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In this paper, we developed a novel high-resolution fifth-order WENO-JS-type scheme that can achieve the optimal accuracy order at or near the arbitrary order critical points. To enhance the accuracy of the weight function of WENO-JS, we normalized the local smoothness factor to obtain a series of normalized variables. By introducing a mapping function that can increase the accuracy of the normalization variables, we developed a new normalized WENO-JS-type scheme called WENO-NSI. The WENO-NSI scheme can improve the shock capture ability by selecting the apposite parameter λ in the mapping function. Numerical experiments of one- and two-dimensional gas dynamic Euler equations for the present WENO-NSI scheme are compared with those of the WENO-JS/Z/M/D/IM and TENO-Z schemes. The results show that the present scheme can achieve theoretical accuracy at or near the arbitrary order critical points, and it has a better shock capturing ability than other schemes. [ABSTRACT FROM AUTHOR]

The WENO-AIM proposed by Vevek et al. [22] can achieve the optimal order for the critical point, and the complex structure of the mapping function of WENO-AIM will substantially increase the computational cost. To reduce the computational cost, we recommended a novel finite-difference mapped WENO method of a rational adaptive operator in this paper. This mapping-type WENO method has a simple framework of achieving the optimal order for critical points of high efficiency. Numerical experiments with one- and two-dimensional benchmark problems of the new mapped method compared with WENO-AIM and other WENO methods. It reveals that the new mapped WENO scheme can further to improve the resolution of WENO-AIM and suppress the numerical oscillation near the discontinuities with higher extra computational efficiency. WENO-AM remains stable with a large CFL number, while WENO-AIM generates non-physical oscillatory. [ABSTRACT FROM AUTHOR]

In this paper, by constructing a selector that can identify the less-smooth sub-stencils, we have improved the classical WENO-JS and WENO-Z schemes, and developed two new WENO schemes which can adaptively increase the weight of less-smooth sub-stencils, WENO-IJS and WENO-IZ. Theoretical analysis shows that the present schemes maintain essentially non-oscillatory (ENO) property and have lower numerical dissipation at discontinuities. The investigation of approximate dispersion relation analysis (ADR) shows that the spectral characteristics of the present schemes are better than those of the classical WENO-JS, WENO-Z and WENO-Z+ schemes. A series of numerical experiments show that the shock wave capture capability and resolution of the complex process structure of the present schemes are significantly better than WENO-JS, WENO-Z and WENO-Z+. [ABSTRACT FROM AUTHOR]