Spatial verification and validation of datasets in fluid dynamics

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Copyright: Watson, Ian Thomas
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Abstract
There is a present need for post-processing tools capable of synthesising and interpreting the numerous spatial data that are typically generated in modern investigations of fluid mechanics. Recent advances have provided both the analyst and the experimentalist with powerful tools for resolving complete flow-field information, using Computational Fluid Dynamics to simulate the flow, or noninvasive flow metrology such as Particle Image Velocimetry and Laser Doppler Anemometry. A great deal of nodal data is generated by these techniques, which quantity may be expected to increase into the future. This data comprises uncertainties in both numerical modelling and experimental measurement, which traditionally have been quantified using classical approaches in Verification and Validation. However, these techniques were designed with summary scalar values in mind and generally overlook or underestimate the importance of suitable spatial and topological description of the flow-field. The author uses established techniques in geostatistics to address the fluids data assimilation problem, and cross-correlate spatial field variables collected over an experimental domain with field variables calculated by a numerical model that simulates this domain. Spatial statistics are generated on the inter-related nodal data, and are used to inform a stationary covariance model describing the datasets as a particular realisation of a random process. This model is used to provide statistics quantifying the correlation of complete experimental and numerical flow-fields, and make better estimations of local field values taking into account the sum data that is available to the practitioner. Special consideration is given to the application of the random function model to a calculated flow-field, in which errors are not aleatoric but epistemic, and comprise unknown chaotic processes and higher-order error terms. The kriging estimator was useful for the characterisation of the spatial datasets considered, and may be expected to extend quite generally to other fluids problems. In particular, meaningful blending of experimental and numerical data was achieved by cokriging, and is demonstrated in situations where experimental data is missing or sparse but may be inferred by the secondary numerical data with which it is well correlated. A statistic describing whole-field correlation on the basis of functional covariance was also proposed for fluids problems, with reference to which it is demonstrated that traditional pointwise measures of disparity are inadequate for spatial problems.
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Author(s)
Watson, Ian Thomas
Supervisor(s)
Barber, Tracie
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Publication Year
2010
Resource Type
Thesis
Degree Type
PhD Doctorate
UNSW Faculty
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