An extremum properties (EP)-based discontinuous sensor and hybrid weighted essentially non-oscillatory scheme on tetrahedral meshes

The high-order weighted essentially non-oscillatory (WENO) schemes are widely used in practical engineering problems due to their excellent shock-capturing features, especially for unstructured meshes. However, its characteristic decomposition and nonlinear weights calculation process bring a lot of computational overhead. Therefore, a hybrid unequal-sized WENO (US-WENO) scheme is developed for hyperbolic conservation laws on tetrahedral meshes. Firstly, an extremum properties (EP)-based discontinuous sensor was designed according to the highest degree polynomial. This proposed discontinuous sensor does not depend on the specific problems and is well adapted to the tetrahedral unstructured meshes in this paper. Secondly, based on the developed EP-based sensor, a hybrid US-WENO scheme was proposed for the first time on three-dimensional unstructured meshes. This method can inherit the excellent features of the US-WENO scheme while improving computational efficiency by about 30% on the same mesh level. Finally, several classical examples are provided to verify the numerical accuracy, shock capture characteristics, and computational efficiency of the proposed method. Numerical results show that the presented method performs well and has a good engineering application prospect.