Near-wall flow deconstruction via mapping and polynomial fit

A mapping technique for enhancing the visualisation and analysis of the flow structure in regions near the wall is presented. After identifying a near-wall region of interest, the output of the proposed mapping technique is an analytical expression of the flow variables, satisfying the governing PDEs and boundary conditions, on a stencil of standardised morphology.

The approach firstly involves selecting a local surface region of interest from the computational domain to be mapped. Subsequently a structured mesh of arbitrary height on top of the cropped surface is generated, thus forming the target volume region, which is termed the physical space. The solution data comprising of flow properties such as velocity and pressure from the computational domain is interpolated onto the physical space. The physical space and the data are consequently mapped onto an unwrapped domain with standard shape, termed the mapped space. For simplicity, the mapped space is chosen here to be a cuboid. Finally, the data is expressed as a best fit polynomial, satisfying the governing PDEs and boundary conditions.

The method is validated by direct pointwise comparison and from the velocity streamlines mapped from the physical space, for a set of test problems. The mapping technique effectiveness is demonstrated firstly on a 90 degree bend pipe as a benchmark investigation and subsequently on a nasal cavity anatomy. For the latter, three scenarios covering different flow structures in the near-wall region are scrutinised, demonstrating the ability of the techniques proposed to uncover the details of the near-wall flow in complex physiological flows. The regions of interest can be identified using near-wall measures such as wall shear stress, shear lines, and wall shear stress critical points.

The mapping technique has potential applications in the fields of fluid dynamics and specifically near-wall flows, as the interface region describing the dynamics of exchanges. It is furthermore capable of inferring the velocity field from reduced data available to enhance the use of deep learning or regression methods.