Accuracy of compact-stencil interpolation algorithms for unstructured mesh finite volume solver

This study considers the accuracy of cell-to-face centre interpolation of convected quantities in unstructured finite volume meshes with cell-centred storage of variables. The accuracy of the interpolation algorithms were tested in isolation using ideal data to determine their numerical accuracy on both standard and artificially distorted meshes. It was found that the formally second- and third-order accurate interpolations based on one-dimensional interpolation along the line connecting the cells to the right and left of the face under consideration only have first-order accuracy in standard unstructured mesh, and less than first-order accuracy in distorted unstructured mesh. L1 interpolation errors in the distorted unstructured mesh are greater than in standard unstructured mesh. The order of accuracy and L1 errors can be improved by applying spatial corrections. The formally second-order accurate multi-dimensional interpolations tested in this study that are not based on one-dimensional interpolation along lines connecting the neighbour cells have first-order accuracy in both standard and distorted unstructured mesh. Linear interpolation between end vertices produces greatest L1 error in standard mesh; polynomial interpolation, linear interpolation between cell centres and standard QUICK produce the greatest L1 error in distorted mesh. Spatially correct QUICK, spatially correct linear interpolation between cell centres, Laplacian interpolation to face centres, and Taylor series expansion about an upstream cell produce the smallest L1 error in both standard and distorted mesh. Based on accuracy and the simplicity of implementation, Taylor series expansion about an upstream cell is the best choice for use in unstructured mesh.