A comprehensive high-order solver verification methodology for free fluid flows

TL;DR

This paper introduces a comprehensive methodology for verifying high-order CFD solvers using manufactured solutions, addressing free flows, curved elements, and turbulence modeling, with practical tools for reproducibility.

Contribution

It develops a set of manufactured solutions tailored for high-order accuracy verification in free fluid flows, including turbulent and curved geometries, and discusses key aspects of code verification methodology.

Findings

Validated high-order accuracy up to sixth order using MSs

Analyzed the impact of grid stretching and self-similarity on discretization errors

Provided reproducible scripts and code for verification procedures

Abstract

The aim of this article is to present a comprehensive methodology for the verification of computational fluid dynamics (CFD) solvers with a special attention to aspects pertinent to discretizations with orders of accuracy (OOAs) higher than two. The method of manufactured solutions (MMS) is adopted and a series of manufactured solutions (MSs) is introduced that examines various components of CFD solvers for free flows (not bounded by walls), including inviscid, laminar and turbulent problems when the latter are modelled by the Reynolds-averaged Navier-Stokes (RANS) equations. The treatment of curved elements is also examined. These MSs are furthermore conceived with demonstrated suitability for the verification of OOAs up to the sixth. Each MS is as well utilized to discuss salient aspects useful to the code verification methodology such as the relative qualities of the most useful norms in measuring the discretization error, the sensitivity analysis of the verification process to forcing function terms, the relation between residual minimization and discretization error convergence in iterative solutions and finally the sensitivity of high-order discretizations to grid stretching and self-similarity. Furthermore, scripts and code are provided as accompanying material to assist the interested reader in reproducing the verification results of each manufactured solution (MS).