Abstract:
Gradients and high-order derivatives reconstruction is an important process for high-order unstructured finite volume (FV) methods, in which the stencil selection plays a critical role. Commonly used stencil selection methods depend on the fixed topology relationship among grid cells, thus the characteristics of flow fields cannot be well captured. Besides, with the improvement of the computational accuracy, the stencil size increases dramatically, yielding redundant stencil cells and low computational efficiency. On this basis, the global-direction stencil developed from the second-order numerical simulations is extended into high-order unstructured finite volume methods to make full use of the spatial extendability and to reduce redundant stencil cells. The effectiveness of this novel stencil is verified by a flow with manufactured solutions and a supersonic vortex flow. Compared with commonly used face-neighbor and vertex-neighbor stencils, the stencil size is considerably reduced, and the computational accuracy is greatly improved. In addition, the stability of this novel stencil is superior to local-direction stencils. As a result, the global-direction stencil has a better numerical performance in the third-order unstructured finite volume methods, and it is feasible to further apply it in high-order numerical simulations.