On the verification of CFD solvers of all orders of accuracy on curved wall-bounded domains and for realistic RANS flows

TL;DR

This paper extends verification methods for high-order CFD schemes on curved walls and turbulent flows, introducing new manufactured solutions and analyzing accuracy, boundary conditions, and turbulence modeling effects up to sixth order.

Contribution

It introduces two new manufactured solutions for verifying high-order schemes on curved domains and turbulent flows, and discusses accuracy, boundary treatment, and turbulence modeling impacts.

Findings

High-order accuracy verified up to sixth order.

New manufactured solutions effectively verify boundary condition treatments.

Analysis of turbulence model effects near walls.

Abstract

This paper aims at extending the code verification methodology to high-order accurate scheme implementations on curved wall-bounded domains as well as for realistic turbulent flows such as the flat plate boundary layer modelled by the Reynolds-averaged Navier-Stokes (RANS) equations. Two new manufactured solutions (MSs) are introduced with demonstrated ability to verify the treatment of slip and no-slip boundary conditions in high-order frameworks on curved domains. These MSs serve as well to discuss the impact of the method of computation of boundary normals on the order of accuracy (OOA) of the solution at the wall. Furthermore, two turbulent boundary layer MSs from literature, devised to mimic the genuine features of RANS-modelled flows in the vicinity of wall, are compared in terms of their suitability to achieving high-order accuracy. A number of useful concepts in verification are explored through these cases such as the limit values of the Spalart-Allmaras (SA) turbulence model source terms at the wall, the verification of the modified vorticity term of the modified SA model, the grid sensitivity of wall-bounded turbulent flows, the inadequacy of substituting solution verification to code verification and the effect of non-dimensionalization of the solution on the minimization of iterative errors via residual convergence. In all cases, demonstrations are carried for orders of accuracy up to the sixth.