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The present study focuses on a reformulation of the Fractional-Step, Artificial Compressibility with Pressure-Projection (FSAC-PP) method by which a diffusion equation for the pressure is obtained through a velocity projection concept. The proposed method is a Fractional-Step Velocity-Projection (FSVP) approach, which is validated for a laminar flow in a lid driven cavity. The results are compared to the classical hyperbolic Artificial Compressibility (AC) method and reference data taken from the literature to demonstrate the strength of the proposed FSVP method.

This study focuses on the investigation of various Godunov-type treatments of the convective fluxes of Navier-Stokes equations by employing a Fractional-Step, Artificial Compressibility and Pressure-Projection (FSAC-PP) formulation. The FSAC-PP approach unifies Chorin's fully-explicit Artificial Compressibility (AC) and semi-implicit Fractional-Step Pressure-Projection (FS-PP) methods for solving the incompressible flow problems. In this work, we study various Riemann solvers by using the FSAC-PP formulation with respect to convergence behaviour and numerical solution accuracies. Furthermore, two benchmark test problems have been investigated as laminar flows in a channel between two parallel flat plates and in a lid-driven cavity. Simulations have been performed at different moderate Reynolds numbers (Re = 100, Re = 400, and Re = 1000) in which cases reference data available in the literature. Numerical solutions have been considered for Rusanov, HLL and HLLC Riemann solvers compared to the case when the Riemann problem is excluded from the numerical procedure. The MUSCL scheme has been employed with a third-order spatial approximation, and fifth-and ninthorder WENO interpolation schemes have also been considered. The computational results have been shown to be very accurate compared to previous studies, and when any Riemann solver is excluded from the numerical procedure.

The flow field around a series of streamwise rods, referred to as canopies, is investigated using two-dimensional two-component time-resolved particle image velocimetry (PIV) and large eddy simulations (LES) to characterize the changes in the flow field responsible for reducing the low and high-frequency surface pressure fluctuations previously observed. It was found that an axisymmetric turbulent boundary layer (ATBL) develops over the rods, whose thickness grows at a greater rate above the rods than below. This boundary layer reaches the wall below the rods at a point where previously a saturation was found in the low-frequency noise attenuation, revealing that the ATBL is responsible for the lowfrequency noise attenuation. The flow is displaced by the presence of the rods, particularly above them, which offset was primarily caused by the blockage of the ATBL. The flow below the rods exhibits the properties of a turbulent boundary layer as its profile still conforms to the logarithmic layer, but the friction velocity was found to drop. This viscous effect was found to be responsible for the high-frequency noise attenuation reported previously.