An unstructured hybrid mesh numerical method is developed to simulate open channel flows. The method is applicable to arbitrarily-shaped mesh cells and offers a framework to unify many mesh topologies into a single formulation. The finite-volume discretization is applied to the two-dimensional depth-averaged St. Venant equations, and the mass conservation is satisfied both locally and globally. An automatic wetting-drying procedure is incorporated in conjunction with the segregated solution procedure that chooses the water surface elevation as the main variable. The method is applicable to both steady and unsteady flows and covers the entire flow range: subcritical, transcritical and supercritical. The proposed numerical method is well suited to natural river flows with a combination of main channels, side channels, bars, floodplains and in-stream structures. Technical details of the method are presented, verification studies are performed using a number of simple flows, and a practical natural river is modeled to illustrate issues of calibration and validation.

The wall shear stress induced by the leaflet motion during the valve-closing phase has been implicated with thrombus initiation with prosthetic valves. Detailed flow dynamic analysis in the vicinity of the leaflets and the housing during the valve-closure phase is of interest in understanding this relationship. A three-dimensional unsteady flow analysis past bileaflet valve prosthesis in the mitral position is presented incorporating a fluid-structure interaction algorithm for leaflet motion during the valve-closing phase. Arbitrary Lagrangian-Eulerian method is employed for incorporating the leaflet motion. The forces exerted by the fluid on the leaflets are computed and applied to the leaflet equation of motion to predict the leaflet position. Relatively large velocities are computed in the valve clearance region between the valve housing and the leaflet edge with the resulting relatively large wall shear stresses at the leaflet edge during the impact-rebound duration. Negative pressure transients are computed on the surface of the leaflets on the atrial side of the valve, with larger magnitudes at the leaflet edge during the closing and rebound as well. Vortical flow development is observed on the inflow (atrial) side during the valve impact-rebound phase in a location central to the leaflet and away from the clearance region where cavitation bubbles have been visualized in previously reported experimental studies.

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The characteristics of near-wall turbulence are examined and the result is used to assess the behaviour of the various terms in the Reynolds-stress transport equations. It is found that all components of the velocity-pressure-gradient correlation vanish at the wall. Conventional splitting of this second-order tensor into a pressure diffusion part and a pressure redistribution part and subsequent neglect of the pressure diffusion term in the modelled Reynolds-stress equations leads to finite near-wall values for two components of the redistribution tensor. This, therefore, suggests that, in near-wall turbulent flow modelling, the velocity-pressure-gradient correlation rather than pressure redistribution should be modelled. Based on this understanding, a methodology to derive an asymptotically correct model for the velocity-pressure-gradient correlation is proposed. A model that has the property of approaching the high-Reynolds-number model for pressure redistribution far away from the wall is derived. A similar analysis is carried out on the viscous dissipation term and asymptotically correct near-wall modifications are proposed. The near-wall closure based on the Reynolds-stress equations and a conventional low-Reynolds-number dissipation-rate equation is used to calculate fully-developed turbulent channel and pipe flows at different Reynolds numbers. A careful parametric study of the model constants introduced by the near-wall closure reveals that one constant in the dissipation-rate equation is Reynolds-number dependent, and a preliminary expression is proposed for this constant. With this modification, excellent agreement with near-wall turbulence statistics, measured and simulated, is obtained, especially the anisotropic behaviour of the normal stresses. On the other hand, it is found that the dissipation-rate equation has a significant effect on the calculated Reynolds-stress budgets. Possible improvements could be obtained by using available direct simulation data to help formulate a more realistic dissipation-rate equation. When such an equation is available, the present approach can again be used to derive a near-wall closure for the Reynolds-stress equations. The resultant closure could give improved predictions of the turbulence statistics and the Reynolds-stress budgets.

A computational fluid dynamic (CFD) analysis is pre sented to describe local flow dynamics in both 3-D spatial and 4-D spatial and temporal domains from reconstructions of intravascular ultrasound (IVUS) and bi-plane angiographic fusion images. A left anterior descending (LAD) coronary artery segment geometry was accurately reconstructed and subsequently its motion was incorporated into the CFD model. The results indicate that the incorporation of motion had appreciable effects on blood flow patterns. The velocity profiles in the region of a stenosis and the circumferential distribution of the axial wall shear stress (WSS) patterns in the vessel are altered with the wall motion introduced in the simulation. The time-averaged axial WSS between simulations of steady flow and unsteady flow without arterial motion were comparable (-0.3 to 13.7 Pa in unsteady flow versus -0.2 to 10.1 Pa in steady flow) while the magnitudes decreased when motion was introduced (0.3-4.5 Pa). The arterial wall motion affects the time-mean WSS and the oscillatory shear index in the coronary vessel fluid dynamics and may provide more realistic predictions on the progression of atherosclerotic disease.