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IN THIS ISSUE

### Research Papers

J. Verif. Valid. Uncert. 2018;3(2):021001-021001-10. doi:10.1115/1.4040803.

This paper presents grid refinement studies for statistically steady, two-dimensional (2D) flows of an incompressible fluid: a flat plate at Reynolds numbers equal to 107, 108, and 109 and the NACA 0012 airfoil at angles of attack of 0, 4, and 10 deg with Re = 6 × 106. Results are based on the numerical solution of the Reynolds-averaged Navier–Stokes (RANS) equations supplemented by one of three eddy-viscosity turbulence models of choice: the one-equation model of Spalart and Allmaras and the two-equation models k – ω SST and $k−kL$. Grid refinement studies are performed in sets of geometrically similar structured grids, permitting an unambiguous definition of the typical cell size, using double precision and an iterative convergence criterion that guarantees a numerical error dominated by the discretization error. For each case, different grid sets with the same number of cells but different near-wall spacings are used to generate a data set that allows more than one estimation of the numerical uncertainty for similar grid densities. The selected flow quantities include functional (integral), surface, and local flow quantities, namely, drag/resistance and lift coefficients; skin friction and pressure coefficients at the wall; and mean velocity components and eddy viscosity at specified locations in the boundary-layer region. An extra set of grids significantly more refined than those proposed for the estimation of the numerical uncertainty is generated for each test case. Using power law extrapolations, these extra solutions are used to obtain an approximation of the exact solution that allows the assessment of the performance of the numerical uncertainty estimations performed for the basis data set. However, it must be stated that with grids up to 2.5 (plate) and 8.46 (airfoil) million cells in two dimensions, the asymptotic range is not attained for many of the selected flow quantities. All this data is available online to the community.

Commentary by Dr. Valentin Fuster
J. Verif. Valid. Uncert. 2018;3(2):021002-021002-10. doi:10.1115/1.4041195.

The Noh verification test problem is extended beyond the commonly studied ideal gamma-law gas to more realistic equations of state (EOSs) including the stiff gas, the Noble-Abel gas, and the Carnahan–Starling EOS for hard-sphere fluids. Self-similarity methods are used to solve the Euler compressible flow equations, which, in combination with the Rankine–Hugoniot jump conditions, provide a tractable general solution. This solution can be applied to fluids with EOSs that meet criterion such as it being a convex function and having a corresponding bulk modulus. For the planar case, the solution can be applied to shocks of arbitrary strength, but for the cylindrical and spherical geometries, it is required that the analysis be restricted to strong shocks. The exact solutions are used to perform a variety of quantitative code verification studies of the Los Alamos National Laboratory Lagrangian hydrocode free Lagrangian (FLAG).

Commentary by Dr. Valentin Fuster

### Technical Brief

J. Verif. Valid. Uncert. 2018;3(2):024501-024501-6. doi:10.1115/1.4041265.

Model verification and validation (V&V) remain a critical step in the simulation model development process. A model requires verification to ensure that it has been correctly transitioned from a conceptual form to a computerized form. A model also requires validation to substantiate the accurate representation of the system it is meant to simulate. Validation assessments are complex when the system and model both generate high-dimensional functional output. To handle this complexity, this paper reviews several wavelet-based approaches for assessing models of this type and introduces a new concept for highlighting the areas of contrast and congruity between system and model data. This concept identifies individual wavelet coefficients that correspond to the areas of discrepancy between the system and model.

Topics: Wavelets , Signals
Commentary by Dr. Valentin Fuster