An efficient hybrid WENO scheme with a problem independent discontinuity locator

Summary In this paper, we have proposed a new problem independent discontinuity locator for hybridization. Along with this, a new global smoothness indicator is proposed. The hybrid weighted essentially nonoscillatory (WENO) scheme works on the principle of applying linear upwind scheme in smooth regions and WENO algorithm in nonsmooth regions to save computational cost, which is reflected in the time taken for the computation of the numerical solution. A problem independent discontinuity locator has been designed based on the properties of the existing smoothness indicators. In addition, to attain the required order of accuracy, a new global smoothness indicator is proposed, which produces a solution with better resolution at discontinuities. Numerical experiments have been included to demonstrate the application of the proposed theory to some benchmark problems. It has been shown that the newly proposed hybrid WENO scheme works faster and gives a solution of higher resolution than WENO‐JS, WENO‐Z, and few other more recent third‐order WENO schemes. To save computational cost and time, the WENO reconstruction is implemented only at the region of discontinuities, which are identified based on newly proposed problem independent discontinuity locator that does not require any threshold assumptions. The global smoothness indicator is proposed that has a lower total variation and hence is expected to give better results. Figure 1 shows located grid points by discontinuity locator in discontinuous and critical point region, whereas Figure 2 shows high resolution result with hybrid WENO scheme for Shu entropy problem.