Johannes V. Soulis

Computation of two-dimensional dam-break- induced flows

Abstract Two-dimensional flood waves resulting from the instantaneous break of dams are numerically examined. The governing system of differential equations is transformed into an equivalent system applied over a square-grid network in order to overcome the difficulties and inaccuracies associated with the determination of flow characteristics near the flow boundaries. The McCormack two-step, predictor-corrector, scheme is used for the solution of the transformed system of equations. Comparisons between computed and experimental data show a satisfactory agreement.

Wall shear stress gradient topography in the normal left coronary arterial tree: possible implications for atherogenesis

SUMMARY Objective: Wall shear stress gradient (WSSG) in vitro has shown its importance in atherogenesis, probably as a local modulator of endothelial gene expression.The purpose of this study is to numerically analyse the WSSG distribution over the normal human left coronary artery (LCA) tree. Research design and methods: A three-dimensional computer generated model of the LCA tree, based on an averaged human data set extracted from angiographies, was adopted for finite-element analysis. The LCA tree includes the left main coronary artery (LMCA), the left anterior descending (LAD), the left circumflex artery (LCxA) and their major branches. Results: In proximal LCA tree regions where atherosclerosis frequently occurs, low WSSG appears. At distal segments, the WSSG increases substantially due to increased velocity resulting from increased vessel tapering. Low WSSG occurs at bifurcations in regions opposite the flow dividers, which are anatomic sites predisposed for atherosclerotic development. Conclusions: This computational work determines, probably for the first time, the topography of the WSSG in the normal human LCA tree. Spatial WSSG differentiation indicates that low values of this parameter probably correlate to atherosclerosis localization. However, further studies are needed to clarify the role of WSSG in atherogenesis.

Wall shear stress on LDL accumulation in human RCAs.

The blood flow and transportation of molecules in the cardiovascular system plays crucial role in the genesis and progression of atherosclerosis. Atherosclerosis shows predilection in regions of the arterial tree with hemodynamic particularities, as local disturbances of wall shear stress in space, and locally high concentrations of lipoprotein. A semi-permeable nature of the arterial wall computational model is incorporated with hydraulic conductivity and permeability treated as wall shear stress dependent. Six image-based human diseased right coronary arteries (RCA) are used to elucidate the low-density lipoprotein (LDL) transport. The 3D reconstruction technique is a combination of angiography and IVUS. The numerical simulation couples the flow equations with the transport equation applying realistic boundary conditions at the wall. The coupling of fluid dynamics and solute dynamics at the endothelium is achieved by the Kedem-Katchalsky equation (water infiltration). The luminal surface LDL concentration at the arterial wall is flow-dependent with local variations due to geometric features. The relationship between WSS and luminal surface concentration of LDL indicates that LDL is elevated at locations where WSS is low. There is medium correlation (Pearson) between low WSS and high LDL. The degree of elevation in luminal surface LDL concentration is mostly affected by the water infiltration velocity at the vessel wall. Under constant water infiltration the shear dependent endothelial permeability effects, in comparison to those using constant value, are marginal. Area-averaged normalized LDL concentration over the RCAs, using constant water infiltration and endothelial permeability is 3.6% higher than that at the entrance. Area-averaged normalized LDL concentration over the RCAs, using shear dependent water infiltration and endothelial permeability is 9.6%. Perspective computational fluid dynamics users, incorporating mass transfer (LDL) within the blood flow, are forced to treat the problem using shear dependent endothelial values.

Low-Density Lipoprotein concentration in the normal Left Coronary Artery tree.

BackgroundThe blood flow and transportation of molecules in the cardiovascular system plays a crucial role in the genesis and progression of atherosclerosis. This computational study elucidates the Low Density Lipoprotein (LDL) site concentration in the entire normal human 3D tree of the LCA.MethodsA 3D geometry model of the normal human LCA tree is constructed. Angiographic data used for geometry construction correspond to end-diastole. The resulted model includes the LMCA, LAD, LCxA and their main branches. The numerical simulation couples the flow equations with the transport equation applying realistic boundary conditions at the wall.ResultsHigh concentration of LDL values appears at bifurcation opposite to the flow dividers in the proximal regions of the Left Coronary Artery (LCA) tree, where atherosclerosis frequently occurs. The area-averaged normalized luminal surface LDL concentrations over the entire LCA tree are, 1.0348, 1.054 and 1.23, for the low, median and high water infiltration velocities, respectively. For the high, median and low molecular diffusivities, the peak values of the normalized LDL luminal surface concentration at the LMCA bifurcation reach 1.065, 1.080 and 1.205, respectively. LCA tree walls are exposed to a cholesterolemic environment although the applied mass and flow conditions refer to normal human geometry and normal mass-flow conditions.ConclusionThe relationship between WSS and luminal surface concentration of LDL indicates that LDL is elevated at locations where WSS is low. Concave sides of the LCA tree exhibit higher concentration of LDL than the convex sides. Decreased molecular diffusivity increases the LDL concentration. Increased water infiltration velocity increases the LDL concentration. The regional area of high luminal surface concentration is increased with increasing water infiltration velocity. Regions of high LDL luminal surface concentration do not necessarily co-locate to the sites of lowest WSS. The degree of elevation in luminal surface LDL concentration is mostly affected from the water infiltration velocity at the vessel wall. The paths of the velocities in proximity to the endothelium might be the most important factor for the elevated LDL concentration.

Relative residence time and oscillatory shear index of non-Newtonian flow models in aorta

Four molecular Non-Newtonian viscosity models plus the Newtonian one were analyzed for the normal human aorta under oscillating flow via: molecular viscosity, time Average Wall Shear Stress (AWSS), Oscillatory Shear Index (OSI) and Relative Residence Time (RRT). The capabilities of the applied non-Newtonian law models appear at low strain rates. The Newtonian blood flow treatment is considered to be a good approximation at mid-and high-strain rates. All blood flow models yield a consistent aorta pattern. High RRT values develop in the concave part of the aortic arch downstream to left subclavian artery. In this region the molecular viscosity is elevated, the WSS is low and the OSI is high. Concave aorta parts are prone to exhibit elevated RRT. The non-Newtonian Power Law blood flow model approximates the molecular viscosity, WSS, OSI and particularly the RRT in a more satisfactory way. High RRT distribution is emerging as an appropriate tool for identifying the possible regions of atheromatic concentrations.

Molecular Viscosity in the Normal Left Coronary Arterial Tree. Is It Related to Atherosclerosis

The purpose of this study is to elucidate, probably for the first time, the distribution of molecular viscosity in the entire left coronary artery (LCA) tree. The governing mass, momentum, and energy flow equations were solved by using a previously validated 3-dimensional numerical (finite-element analysis) code. High-molecular-viscosity regions occur at bifurcations in regions opposite the flow dividers, which are anatomic sites predisposed for atherosclerotic development. Furthermore, high-molecular-viscosity values appear in the proximal regions of the LCA tree, where atherosclerosis frequently occurs. The effect of blood flow resistance, due to increased blood viscosity, gives rise to increased contact time between the atherogenic particles of the blood and the endothelium, probably promoting atherosclerosis. Observations suggest that, whole viscosity distribution within the coronary artery tree may represent a risk factor for the resulting atherosclerosis. This distribution can become a possible tool for the location of atherosclerotic lesions.

A numerical method for torsional analysis of structural elements

Abstract An efficient numerical algorithm for two-dimensional structural element torsional analysis has been developed. The developed algorithm utilizes a numerical mapping and has no requirement of extended computing power since it does not make use of any stiffness matrix inversion calculation. The scheme preserves the practicability of the finite element method in treating irregular boundaries while it makes use of the simple analysis of the finite difference method. Therefore, a transformed torsional equation in the local system for a structural element consisting of more than one material is derived. For concrete elements, concrete cracking is also taken into consideration. Comparisons of the predicted results with analytical solutions for cross-sections of various shapes indicate that the proposed two-dimensional finite volume approach of the torsional problem is accurate, reliable and fast. Comparisons of the predicted results with available experimental data for reinforced concrete elements indicate that before the occurrence of concrete cracking the results are relatively good. For tested concrete elements having longitudinal bars as reinforcement, the computed torsional rigidity and ultimate torque moment appear to be lower than the measured values.

Molecular viscosity distribution in the left coronary artery tree

The purpose of this study is to elucidate, probably for the first time, the distribution of the molecular viscosity in the entire left coronary artery (LCA) tree. A three-dimensional computer model of the normal LCA tree, reported previously, was adopted for subsequent numerical analysis. The governing mass, momentum and energy flow equations were solved using a previously validated numerical (finite-element analysis) code. The calculated results show high molecular viscosity regions appearing in zones opposite to all left coronary artery flow dividers on either of the two sides. These are regions where atherosclerotic plaques usually develop. Viscosity values change throughout the flow field. The distribution of high molecular viscosity along the walls is in agreement with the prone to atherosclerosis regions.

A Numerical Method for 2-D Bed Morphology Calculations

A fully coupled two-dimensional sub-critical and/or supercritical, free-surface flow numerical model is developed to calculate bed variations in alluvial channels. Vertically averaged free-surface flow equations in conjunction with sediment transport equation are numerically solved using an explicit finite-volume scheme in integral form. The capabilities of the proposed method are first demonstrated by analyzing supercritical flow in an expansion channel. Thereafter, one and two-dimensional applications referring to aggradation and scouring are reported. For each of these test cases, computed results compare satisfactorily with measurements as well as with other numerical solutions. The method is stable, reliable and accurate, although time consuming, handling a variety of sediment transport equations with rapid changes of sediment transport at the boundaries.

Multiple grid solution of the open channel flow equations using a marching finite-volume method

Abstract A multi-grid algorithm has been developed to accelerate the convergence solution of the open channel flow equations to obtain the steady flow. The scheme is constructed by combining the multiple-grid technique with a new marching finite-volume numerical solution. In the multi-grid application the corrections to the fine grid points are transferred to a coarse grid to maintain the low truncation errors associated with a fine level of discretizations. Distribution formulae are then used to propagate the changes onto selected coarser grid points. After applying interpolation to coarse grid corrections, the flow properties at every grid point of the fine mesh are updated. The channel flow will be assumed to be 2D, steady and viscous with wind and Coriolis forces neglected. The flow is also assumed to be fully mixed in the vertical direction. The general technique used is a combination of the finite-element and finite-difference methods. The governing PDE are transformed into an equivalent system applied over a square-grid network. Convergence histories are presented for supercritical flows as well as for super-critical flows with hydraulic jump presence. Numerical results indicate that substantial computational savings for the solution accuracy can be achieved.