No . 2007-08 Accuracy Analysis for Mixed-Element Finite-Volume Discretization Schemes

A new computational analysis tool, downscaling (DS) test, has been introduced and applied for studying the convergence rates of truncation and discretization errors of finite-volume discretization (FVD) schemes on general unstructured grids. The study corrects a misconception that the discretization accuracy of FVD schemes on irregular grids is directly linked to convergence of truncation errors. The DS test is a general, efficient, accurate, and practical tool, enabling straightforward extension of verification and validation to general unstructured grid formulations. It also allows separate analysis of the interior, boundaries, and singularities that could be useful even in structured-grid settings. There are several new findings arising from the use of the DS test analysis. It was shown that the discretization accuracy of a common nodecentered FVD scheme, known to be second-order accurate for inviscid equations on triangular grids, degenerates to first order for certain mixed-element grids. Alternative node-centered schemes have been presented and demonstrated to provide second and third order accuracies on general mixed-element grids. The local accuracy deterioration at intersections of tangency and inflow/outflow boundaries has been demonstrated using the DS tests tailored to examining the local behavior of the boundary conditions. The discretization-error order reduction within inviscid stagnation regions has been demonstrated. The accuracy deterioration is local, affecting mainly the velocity components, but applies to any order scheme.