Improvement of the WENO-NIP Scheme for Hyperbolic Conservation Laws

The WENO-NIP scheme was obtained by developing a class of L1-norm smoothness indicators based on Newton interpolation polynomial. It recovers the optimal convergence order in smooth regions regardless critical points and achieves better resolution than classical WENO-JS scheme. However, produces severe spurious oscillations when solving 1D linear advection problems with discontinuities at long output times, it is also very oscillatory near for Riemann problems. In this paper, we find that spectral property exhibits negative dissipation characteristic, reason why unstable discontinuities. Using knowledge, develop way improving introducing an additional term to eliminate interval. proposed scheme, denoted as WENO-NIP+, maintains same property, well low-dissipation corresponding Numerical examples confirm much more stable large times Furthermore, new far less dissipative region high-frequency waves. addition, improved WENO-NIP+ can remove or least greatly decrease post-shock are commonly produced simulating 2D Euler equations strong shocks.