Third-order WENO schemes with kinetic flux vector splitting

摘要

The numerical methods for solving the hyperbolic conservation laws are mainly based on the upwinding principle. The weighted essentially nonoscillatory (WENO) schemes are among the most commonly used numerical schemes for solving the hyperbolic conservation laws due to their nonoscillatory property and high order good shock capturing abilities. The upwinding principle requires the splitting of the flux into its positive and negative parts. WENO schemes have so far been widely implemented using the Lax Friedrich flux vector splitting technique for splitting purpose. In this article, we have implemented them with the kinetic flux vector splitting (KFVS) technique. The comparison has been made with both flux vector splitting techniques for one dimensional Euler equations. The results obtained are as expected, considerable improvement has been seen in the solution obtained by the scheme which has been implemented with the kinetic flux vector splitting. The reason being KFVS is based on the sign of the intermolecular particle velocity, which is a physical quantity.