On the balance between robustness and accuracy in finite-volume codes

Today, finite-volume codes used in the maritime industry can compute the flow around complicated geometries using unstructured, body-fitted computational meshes with arbitrary polyhedral cells. In many cases, such meshes contain hanging nodes, especially near the borders of refinement boxes, which cause eccentricity and/or non-orthogonality in the mesh. An example of a mesh containing hanging nodes is shown in Fig. 1. For such meshes, correction methods for eccentricity and non-orthogonality in the cell-to-face interpolation improve the order of mesh convergence. However, these correction methods can cause robustness issues for applications with complicated geometries, especially when those geometries contain sharp corners. This paper describes how such correction methods can be implemented, what their effect is on the robustness, how the robustness can be improved and what effect these robustness improvements can have on the accuracy.