An improved two-dimensional unstructured CE/SE scheme for capturing shock waves

In this paper, the accuracy of Chang’s unstructured space–time conservation element and solution element (CE/SE) scheme is analysed for the first time. Based on a redefinition of conservation elements and solution elements, an improved two-dimensional (2D) unstructured CE/SE scheme with an adjustable parameter β is proposed to accurately capture shock waves. The new scheme can be applied to any type of grid without special treatment. Compared with Chang’s original parameter α, larger β dose not cost extra computational resources. Numerical tests reveal that the new scheme is not only clear in physical concept, compact and highly accurate but also more capable of capturing shock waves than the popular fifth-order accurate weighted essentially non-oscillatory scheme.