Improvement On Mapped Weights Function Of WENO Scheme

A new kind of high order resolution numerical scheme is constructed to solvehyperbolic conservation laws in this paper, the newly designed WENO method isimproved through a mapped function that satisfies certain conditions. This function canredistribute weights corresponds to every template. Compared to original mappedfunction, it will distribute more range to smooth area that is close to ideal weights.Through numerical experiments and analysis of WENO-PM scheme, we choose anappropriate point to distinguish smooth area and discontinuous area, and enlargediscontinuous area a little, then we certificate that WENO-DM scheme can reachoptimal order convergence. Finally we apply this WENO scheme to standard test codeof high resolution method, obtain a result with faster convergence speed and less error,when there are shocks, contact discontinuity or complex smooth flow, we can seeclearly that numerical dissipation is less than WENO-JS scheme, so does spuriousoscillation, and it performs good where exists large gradient. The new designedmapped function can adjust easily to be applied to any order WENO scheme bychanging ideal weights, so that around smooth extreme points we still can obtainoptimal order convergence. As usual, we need emphasize that WENO-DM schemecan’t give good proof about stability, Etc. But numerical tests show that this schemekeep good robustness and reliability, at the same time, obtain better convergence result.