(untitled) (Advances in Applied Mathematics and Mechanics, 2024)
In this paper, a new high-resolution WENO-MIM scheme that can achieve optimal accuracy at high-order critical points is developed. The nonlinear weight function of the new scheme can be obtained by adding a freely adjustable term with a parameter λ to the mapping function of the WENO-IM scheme. A sufficient condition shows the shock-capturing ability of WENO-MIM will be enhanced with the increase of λ. The parameter λ=467 obtained from experience can guarantee the new scheme achieves high resolution. Numerical example results show that the present scheme can achieve optimal accuracy at high-order critical points and perform significantly better than other WENO schemes in highly efficient computing of various compressible fluid problems.