An efficient scaling of WENO-JS weights for accuracy preserving and higher resolution schemes

Abstract

In this short paper, we present efficient scaling of WENO-JS weights which results in robust and formal accuracy preserving high resolution WENO-JS schemes. The proposed scaling makes the WENO-JS schemes robust in the sense that schemes works well irrespective of the choice for the parameter ϵ used in classical WENO-JS weights to prevent division by zero. In smooth solution region the proposed scaling keeps the scaled WENO weights in the vicinity of critical weights thus resulting scheme retains formal accuracy. Numerical experiments show that the WENO schemes with scaled weights provide higher resolution for discontinuities as well for smooth solution with high gradients.