High-resolution WENO-Z type scheme with mapped global smoothness indicator for hyperbolic conservation laws

To address the shortcomings of the WENO-Z scheme in terms of reducing accu-racy at higher-order critical points, this paper proposes a new two-parameter global smoothing factor by introducing a sub-stencil mapping function anddevelops a new WENO-Z scheme, WENO-ZI. With the chosen parameters q <= 2 and lambda > 0, the new scheme can achieve the desired accuracy at criticalpoints of any order, and the resolution is enhanced as lambda increases. Numeri-cal results indicate that the new scheme performs optimally whenq=2and lambda=4for one-dimensional problems, and lambda=13for two-dimensional prob-lems. The theoretical results verify the high accuracy and high-resolution of thenew WENO-ZI scheme. Numerical experiments of the new mapping methodfor one- and two-dimensional benchmark problems are compared with variousnumerical schemes. Results demonstrate that the new WENO scheme achieveshigher resolution compared to other numerical methods. It satisfies the desiredaccuracy at critical points of arbitrary orders and can be easily extended tohigher-order schemes.