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

Abstract

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 does 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.

Simulation of shock-induced instability using an essentially conservative adaptive CE/SE method

“…In our AMR implementation, non-conservation due to different neighboring cell sizes is eliminated by an extension of CEs and SEs in Ref. [18]. High discontinuity resolution is also obtained using optimized interpolations.…”

“…According to Ref. [18], our redefinition eliminates conservative errors by different cell sizes. During the simulation, the time step is the same for all SPs.…”

“…In this work, an essentially conservative adaptive CE/SE (ECA-CE/SE) scheme with less computational cost and conservative error is established as a consistent extension of a variant high resolution unstructured CE/SE scheme. [18] The redefined conservation elements (CEs) and solution elements (SEs), and optimized interpolations are essential parts of our implementation. In the following paragraphs, we will give a detailed description of the ECA-CE/SE scheme.…”

Three-dimensional detonation cellular structures in rectangular ducts using an improved CESE scheme

“…[29] As a result, it not only has a good shock capturing capacity, but also can be used to simulate acoustic waves. [30] In order to solve problems with complex boundary conditions as well as with a lower expense of computational resource, unstructured [31] and essentially conservative adaptive [32] definition of CEs can be also employed. But these improved schemes will lose some degree of global conservativeness.…”

An improved global-direction stencil based on the face-area-weighted centroid for the gradient reconstruction of unstructured finite volume methods*

“…[1] Compared with the structured grid, [2] this kind of grids is easy to generate without heavily manual intervention, and has a better adaptability to different engineering shapes. [3][4][5][6] Therefore, compared with the block-structured grid, utilizing unstructured grid brings a lot of flexibilities. [7] Nowadays, the most widely used algorithms for unstructured grids are second-order finite volume methods (FVM) [8][9][10] adopted by many well-known software packages, such as Ansys's fluent (http://www.ansys.com) and the open source software OpenFOAM (http://openfoam.org), and the accuracy of these algorithms is greatly influenced by the gradient reconstruction, for which the stencil selection plays a critical role.…”