Improvements of the fifth-order WENO-JS-type scheme with normalized smoothing factor for gas dynamic Euler equations
In this paper, a fifth-order WENO-JS-type scheme is developed that can achieve a theoretical optimal accuracy at high-order critical points. The WENO-NSI scheme is constructed using (a) normalizing the local smoothness factor to obtain three normalized variables, (b) introducing a mapping function to improve the accuracy of the normalized variables, and (c) dividing the linear weights using a mapping function. Numerical experiments of one- and two-dimensional gas dynamic Euler equations show that WENO-NSI scheme can reduce to the third- or even second-order at or near the higher-order critical point, compared with the classical WENO-JS/Z/M/D/IM and TENO-Z schemes and it has a better shock-capturing ability than other schemes.
scientific article; zbMATH DE number 7630336
scientific article