An improved hybridization strategy for the fifth-order unequal-sized weighted essentially non-oscillatory scheme

Abstract

In this paper, a hybrid unequal-sized weighted essentially non-oscillatory (US-WENO) scheme is developed to reduce the computational cost caused by the computation of nonlinear weights and local characteristic decompositions in its procedures. First, an improved discontinuous sensor is designed based on the mathematical properties of the fourth-degree reconstruction polynomial in the US-WENO scheme. The proposed hybridization strategy can automatically and efficiently identify the troubled cells, and does not contain artificial parameters related to the problems. Second, the efficient linear scheme and the existing US-WENO scheme are combined to simulate the inviscid and viscous compressible flow problems. Finally, some benchmark numerical examples are used to verify the performance of the presented hybrid WENO scheme in various aspects, such as computational efficiency, low dissipation characteristics, shock capture ability, etc. The numerical experiments show that the proposed hybrid method can inherit all the features of the existing US-WENO scheme while improving its computational efficiency.