THE INFLUENCE OF GLOBAL-DIRECTION STENCIL ON GRADIENT AND HIGH-ORDER DERIVATIVES RECONSTRUCTION OF UNSTRUCTURED FINITE VOLUME METHODS 1)

The accuracy of unstructured finite volume methods is greatly influenced by different stencils. In previous work, based on the existing problems of local-direction stencil, we explored a more concise global-direction stencil selection method for the second-order unstructured finite volume solver, and stencil cells selected by this novel stencil selection method are always along the boundary normal and circumferential directions even on grids with high aspect ratio. As a result, the variation of flowfield is effectively captured, and flow anisotropy are well reflected. In addition, the novel method is topology-independent, since global directions are determined by the flowfield, while the local directions are strongly coupled with the grid. Therefore, the complex process of advancing front as well as local directions estimation are completely avoided in the novel stencil selection method, and the phenomenon that stencil cells deviate from the boundary normal vector is effectively eliminated on high-aspect-ratio triangular grids. What's more, a better computational accuracy and lower truncation errors on the second-order accurate finite volume solver are obtained by the employment of global-direction stencil. In order to further test the effectiveness of global-direction stencil on high-order unstructured finite volume methods, we will preliminarily utilize this stencil to test the effect of gradient and high-order derivatives reconstruction. After verification, computational errors of global-direction stencil are lower than that of local-direction stencil, and also lower than that of commonly used vertex-neighbor stencil on different grid types. Besides, errors of variable and derivatives at the Gauss point obtained by global-direction stencil are also the lowest among three methods we tested. Therefore, the global-direction stencil is well performed on gradient as well as high-order derivatives reconstruction, and it is feasible to extend this novel stencil selection method to high-order unstructured finite volume methods.