Part 1 of this two-part paper presents a comprehensive approach to verification and validation methodology and procedures for CFD simulations from an already developed CFD code applied without requiring availability of the source code for specified objectives, geometry, conditions, and available benchmark information. Concepts, definitions, and equations derived for simulation errors and uncertainties provide the overall mathematical framework. Verification is defined as a process for assessing simulation numerical uncertainty and, when conditions permit, estimating the sign and magnitude of the numerical error itself and the uncertainty in that error estimate. The approach for estimating errors and uncertainties includes (1) the option of treating the numerical error as deterministic or stochastic, (2) the use of generalized Richardson extrapolation for J input parameters, and (3) the concept of correction factors based on analytical benchmarks, which provides a quantitative metric to determine proximity of the solutions to the asymptotic range, accounts for the effects of higher-order terms, and are used for defining and estimating errors and uncertainties. Validation is defined as a process for assessing simulation modeling uncertainty by using benchmark experimental data and, when conditions permit, estimating the sign and magnitude of the modeling error itself. The approach properly takes into account the uncertainties in both the simulation and experimental data in assessing the level of validation. Interpretation of results of validation efforts both where the numerical error is treated as deterministic and stochastic are discussed. Part 2 provides an example for RANS simulations for a cargo/container ship where issues with regard to practical application of the methodology and procedures and interpretation of verification and validation results are discussed.

Reynolds-averaged Navier-Stokes (RANS) equations are widely used in engineering turbulent flow simulations. However, RANS predictions may have large discrepancies due to the uncertainties in modeled Reynolds stresses. Recently, Wang et al. demonstrated that machine learning can be used to improve the RANS modeled Reynolds stresses by leveraging data from high fidelity simulations (Physics informed machine learning approach for reconstructing Reynolds stress modeling discrepancies based on DNS data. Physical Review Fluids. 2, 034603, 2017). However, solving for mean flows from the improved Reynolds stresses still poses significant challenges due to potential ill-conditioning of RANS equations with Reynolds stress closures. Enabling improved predictions of mean velocities are of profound practical importance, because often the velocity and its derived quantities (QoIs, e.g., drag, lift, surface friction), and not the Reynolds stress itself, are of ultimate interest in RANS simulations. To this end, we present a comprehensive framework for augmenting turbulence models with physics-informed machine learning, illustrating a complete workflow from identification of input features to final prediction of mean velocities. This work has two innovations. First, we demonstrate a systematic procedure to generate mean flow features based on the integrity basis for mean flow tensors. Second, we propose using machine learning to predict linear and nonlinear parts of the Reynolds stress tensor separately. Inspired by the finite polynomial representation of tensors in classical turbulence modeling, such a decomposition is instrumental in overcoming the ill-conditioning of RANS equations.Numerical tests demonstrated merits of the proposed framework.

The canine nasal cavity contains hundreds of millions of sensory neurons, located in the olfactory epithelium that lines convoluted nasal turbinates recessed in the rear of the nose. Traditional explanations for canine olfactory acuity, which include large sensory organ size and receptor gene repertoire, overlook the fluid dynamics of odorant transport during sniffing. But odorant transport to the sensory part of the nose is the first critical step in olfaction. Here we report new experimental data on canine sniffing and demonstrate allometric scaling of sniff frequency, inspiratory airflow rate and tidal volume with body mass. Next, a computational fluid dynamics simulation of airflow in an anatomically accurate three-dimensional model of the canine nasal cavity, reconstructed from high-resolution magnetic resonance imaging scans, reveals that, during sniffing, spatially separate odour samples are acquired by each nostril that may be used for bilateral stimulus intensity comparison and odour source localization. Inside the nose, the computation shows that a unique nasal airflow pattern develops during sniffing, which is optimized for odorant transport to the olfactory part of the nose. These results contrast sharply with nasal airflow in the human. We propose that mammalian olfactory function and acuity may largely depend on odorant transport by nasal airflow patterns resulting from either the presence of a highly developed olfactory recess (in macrosmats such as the canine) or the lack of one (in microsmats including humans).

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The canine nasal airway is an impressively complex anatomical structure, having many functional roles. The complicated branching and intricate scrollwork of the nasal conchae provide large surface area for heat, moisture, and odorant transfer. Of the previous anatomical studies of the canine nasal airway, none have included a detailed rendering of the maxilloturbinate and ethmoidal regions of the nose. Here, we present a high-resolution view of the nasal airway of a large dog, using magnetic resonance imaging scans. Representative airway sections are shown, and a three-dimensional surface model of the airway is reconstructed from the image data. The resulting anatomic structure and detailed morphometric data of the airway provide insight into the functional nature of canine olfaction. A complex airway network is revealed, wherein the branched maxilloturbinate and ethmoturbinate scrolls appear structurally distinct. This is quantitatively confirmed by considering the fractal dimension of each airway, which shows that the maxilloturbinate airways are more highly contorted than the ethmoidal airways. Furthermore, surface areas of the maxilloturbinate and ethmoidal airways are shown to be much different, despite having analogous physiological functions. Functionally, the dorsal meatus of the canine nasal airway is shown to be a bypass for odorant-bearing inspired air around the complicated maxilloturbinate during sniffing for olfaction. Finally, nondimensional analysis is used to show that the airflow within both the maxilloturbinate and ethmoturbinate regions must be laminar. This work has direct relevance to biomimetic sniffer design, chemical trace detector development, intranasal drug delivery, and inhalation toxicology.