A case-study in open-source CFD code verification. Part II: Boundary condition non-orthogonal correction
Abstract This investigation constitutes the follow-up to a previous work in which we applied the manufactured solution procedure to verify the OpenFOAM diffusion operator on different types of meshes. Theoretical convergence orders were observed for Poisson’s equation solver on orthogonal hexahedral grids using several boundary conditions. We noticed that on non-orthogonal grids even slight mesh distortions reduce the theoretical second order convergence rate to first order. Our investigation showed that this loss in convergence order takes place when Dirichlet and/or Neumann boundary conditions are used on non-orthogonal meshes. In this paper, we introduce ways to achieve theoretical second order convergence accuracy, mainly based on applying non-orthogonal correction to Dirichlet and/or Neumann boundary condition schemes. A peculiarity was discovered for the Least-Squares gradient scheme that slightly affects second-order convergence, and which we attribute to the non-orthogonal correction at boundaries in the Least-Squares vector reconstruction library. The verification procedure is performed using the method of manufactured solutions for the Poisson equation and an analytical solution, the SIMPLE solver, for the Navier–Stokes equations. The average and maximum error norms were used to calculate the convergence rate. Comparative results are presented.
Verification of Codes and Calculations
Background discussion, definitions, and descriptions are given for some terms related to confidence building in computational fluid dynamics. The two principal distinctions made are between verification vs validation and between verification of codes vs verification of individual calculations. Also discussed are numerical errors vs conceptual modeling errors; iterative convergence vs grid convergence (or residual accuracy vs discretization accuracy); confirmation, calibration, tuning, and certification; error taxonomies; and customer illusions vs customer care. Emphasis is given to rigorous code verification via systematic grid convergence using the method of manufactured solutions, and a simple method for uniform reporting of grid convergence studies using the Grid Convergence Index (GCI). Also discussed are surrogate single-grid error indicators.
SIERRA/Premo-A New General Purpose Compressible Flow Simulation Code
This paper reports on the progress of a new compressible flow simulation code being developed at Sandia National Laboratories. The code called Premo is a CFD module that is part of a much larger multimechanics code framework called SIERRA. The goal of the Premo project is to deliver a general purpose CFD capability for designers and analysts of aerodynamics of flight vehicles. SIERRA provides unstructured mesh data services common to many computational mechanics codes. Utilizing the framework allows for rapid development of physics modules. In addition, the SIERRA framework provides an interface that will make it possible to conduct multiphysics simulations between physics modules to solve such problems as aero-thermal vehicle heating and aero elasticity in the future. Current code capabilities are demonstrated by solving one-, two- and threedimensional flow problems.