A high-efficiency and low-dissipation hybrid weighted essentially non-oscillatory scheme

TL;DR

This paper introduces a hybrid WENO scheme that enhances computational efficiency and reduces numerical dissipation by adaptively switching between WENO and linear fluxes based on a discontinuity detector.

Contribution

It presents a novel hybrid approach that combines WENO and linear schemes for improved efficiency and accuracy in solving hyperbolic conservation laws.

Findings

Achieves very small numerical dissipation

Maintains good robustness

Negligible additional computational effort

Abstract

In this paper, we propose a simple hybrid WENO scheme to increase computational efficiency and decrease numerical dissipation. Based on the characteristic-wise approach, the scheme switches the numerical flux of each characteristic variables between that of WENO scheme and its optimal linear scheme according to a discontinuity detector measuring the non-resolvability of the linear scheme. A number of numerical examples computed with 5th-order WENO scheme suggested that, while achieving very small numerical dissipation and good robustness, the computational effort on WENO flux used in the hybrid scheme is negligible.