Abstract
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.
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