53 results found
Witherden FD, Vincent PE, 2014, An Analysis of Solution Point Coordinates for Flux Reconstruction Schemes on Triangular Elements, JOURNAL OF SCIENTIFIC COMPUTING, Vol: 61, Pages: 398-423, ISSN: 0885-7474
Witherden FD, Farrington AM, Vincent PE, 2014, PyFR: An open source framework for solving advection-diffusion type problems on streaming architectures using the flux reconstruction approach, COMPUTER PHYSICS COMMUNICATIONS, Vol: 185, Pages: 3028-3040, ISSN: 0010-4655
De Grazia D, Mengaldo G, Moxey D, et al., 2014, Connections between the discontinuous Galerkin method and high-order flux reconstruction schemes, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Vol: 75, Pages: 860-877, ISSN: 0271-2091
, 2014, A guide to the implementation of boundary conditions in compact high-order methods for compressible aerodynamics
The nature of boundary conditions, and how they are implemented, can have a significant impact on the stability and accuracy of a Computational Fluid Dynamics (CFD) solver. The objective of this paper is to assess how different boundary conditions impact the performance of compact discontinuous high-order spectral element methods (such as the discontinuous Galerkin method and the Flux Reconstruction approach), when these schemes are used to solve the Euler and compressible Navier-Stokes equations on unstructured grids. Specifically, the paper will investigate inflow/outflow and wall boundary conditions. In all studies the boundary conditions were enforced by modifying the boundary flux. For Riemann invariant (characteristic), slip and no-slip conditions we have considered a direct and an indirect enforcement of the boundary conditions, the first obtained by calculating the flux using the known solution at the given boundary while the second achieved by using a ghost state and by solving a Riemann problem. All computations were performed using the open-source software Nektar++ (www.nektar.info).
Wang ZJ, Huynh HT, Vincent PE, 2013, High-Order Methods for Computational Fluid Dynamics: A Brief Review of Compact Differential Formulations on Unstructured Grids, Computers and Fluids
Castonguay P, Williams DM, Vincent PE, et al., 2013, Energy stable flux reconstruction schemes for advection-diffusion problems, COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, Vol: 267, Pages: 400-417, ISSN: 0045-7825
Vincent PE, Weinberg PD, 2013, Flow-Dependent Concentration Polarization and the Endothelial Glycocalyx Layer: Multi-Scale Aspects of Arterial Mass Transport and their Implications for Atherosclerosis, Biomech Model Mechanobiol
Atherosclerosis is the underlying cause of most heart attacks and strokes. It is thereby the leading cause of death in the Western world, and it places a significant financial burden on health care systems. There is evidence that complex, multi-scale arterial mass transport processes play a key role in the development of atherosclerosis. Such processes can be controlled both by blood flow patterns and by properties of the arterial wall. This short review focuses on one vascular-scale, flow-regulated arterial mass transport process, namely concentration polarization of low density lipoprotein at the luminal surface of the arterial endothelium, and on one cellular-scale, structural determinant of arterial wall mass transport, namely the endothelial glycocalyx layer. Both have attracted significant attention in recent years. In addition to reviewing and appraising relevant literature, we propose various directions for future work.
Corbett R, Demicheli N, Iori F, et al., 2013, Novel Approach to Reduce the Burden of Neointimal Hyperplasia in Arteriovenous Fistulae, 50th European-Renal-Association - European-Dialysis-and-Transplant-Association Congress, Publisher: OXFORD UNIV PRESS, Pages: 229-229, ISSN: 0931-0509
Castonguay P, Williams DM, Vincent PE, et al., 2013, Energy Stable Flux Reconstruction Schemes for Advection-Diffusion Problems, Computer Methods in Applied Mechanics and Engineering
Castonguay P, Vincent PE, Jameson A, 2012, A New Class of High-Order Energy Stable Flux Reconstruction Schemes for Triangular Elements, Journal of Scientific Computing, Vol: 55, Pages: 224-256
Jameson A, Vincent PE, Castonguay P, 2012, On the Non-linear Stability of Flux Reconstruction Schemes, Journal of Scientific Computing, Vol: 50, Pages: 434-445, ISSN: 0885-7474
The flux reconstruction (FR) approach unifies various high-order schemes, including collocation based nodal discontinuous Galerkin (DG) methods, and all spectral difference methods (at least for a linear flux function), within a single framework. Recently a new range of linearly stable FR schemes have been identified, henceforth referred to as Vincent-Castonguay-Jameson-Huynh (VCJH) schemes. In this short note non-linear stability properties of FR schemes are elucidated via analysis of linearly stable VCJH schemes (so as to focus attention solely on issues of non-linear stability). It is shown that linearly stable VCJH schemes (at least in their standard form) may be unstable if the flux function is non-linear. This instability is due to aliasing errors, which manifest since FR schemes (in their standard form) utilize a collocation projection at the solution points to construct a polynomial approximation of the flux. Strategies for minimizing such aliasing driven instabilities are discussed within the context of the FR approach. In particular, it is shown that the location of the solution points will have a significant effect on non-linear stability. This result is important, since linear analysis of FR schemes implies stability is independent of solution point location. Finally, it is shown that if an exact L2 projection is employed to construct an approximation of the flux (as opposed to a collocation projection), then aliasing errors and hence aliasing driven instabilities will be eliminated. However, performing such a projection exactly, or at least very accurately, would be more costly than performing a collocation projection, and would certainly impact the inherent efficiency and simplicity of the FR approach. It can be noted that in all above regards, non-linear stability properties of FR schemes are similar to those of nodal DG schemes. The findings should motivate further research into the non-linear performance of FR schemes, which have hitherto been devel
Vincent PE, Plata AM, Hunt AAE, et al., 2011, Blood Flow in the Rabbit Aortic Arch and Descending Thoracic Aorta, Journal of the Royal Society Interface, Vol: 8, Pages: 1708-1719, ISSN: 1742-5689
The distribution of atherosclerotic lesions within the rabbit vasculature, particularly within the descending thoracic aorta, has been mapped in numerous studies. The patchy nature of such lesions has been attributed to local variation in the pattern of blood flow. However, there have been few attempts to model and characterize the flow. In this study, a high-order continuous Galerkin finite-element method was used to simulate blood flow within a realistic representation of the rabbit aortic arch and descending thoracic aorta. The geometry, which was obtained from computed tomography of a resin corrosion cast, included all vessels originating from the aortic arch (followed to at least their second generation) and five pairs of intercostal arteries originating from the proximal descending thoracic aorta. The simulations showed that small geometrical undulations associated with the ductus arteriosus scar cause significant deviations in wall shear stress (WSS). This finding highlights the importance of geometrical accuracy when analysing WSS or related metrics. It was also observed that two Dean-type vortices form in the aortic arch and propagate down the descending thoracic aorta (along with an associated skewed axial velocity profile). This leads to the occurrence of axial streaks in WSS, similar in nature to the axial streaks of lipid deposition found in the descending aorta of cholesterol-fed rabbits. Finally, it was observed that WSS patterns within the vicinity of intercostal branch ostia depend not only on local flow features caused by the branches themselves, but also on larger-scale flow features within the descending aorta, which vary between branches at different locations. This result implies that disease and WSS patterns in the vicinity of intercostal ostia are best compared on a branch-by-branch basis.
Vincent PE, Castonguay P, Jameson A, 2011, Insights from von Neumann Analysis of High-Order Flux Reconstruction Schemes, Journal of Computational Physics, Vol: 230, Pages: 8134-8154
Vincent PE, Castonguay P, Jameson A, 2011, A New Class of High-Order Energy Stable Flux Reconstruction Schemes, Journal of Scientific Computing, Vol: 47, Pages: 50-72, ISSN: 0885-7474
The flux reconstruction approach to high-order methods is robust, efficient, simple to implement, and allows various high-order schemes, such as the nodal discontinuous Galerkin method and the spectral difference method, to be cast within a single unifying framework. Utilizing a flux reconstruction formulation, it has been proved (for one-dimensional linear advection) that the spectral difference method is stable for all orders of accuracy in a norm of Sobolev type, provided that the interior flux collocation points are located at zeros of the corresponding Legendre polynomials. In this article the aforementioned result is extended in order to develop a new class of one-dimensional energy stable flux reconstruction schemes. The energy stable schemes are parameterized by a single scalar quantity, which if chosen judiciously leads to the recovery of various well known high-order methods (including a particular nodal discontinuous Galerkin method and a particular spectral difference method). The analysis offers significant insight into why certain flux reconstruction schemes are stable, whereas others are not. Also, from a practical standpoint, the analysis provides a simple prescription for implementing an infinite range of energy stable high-order methods via the intuitive flux reconstruction approach.
Vincent PE, Jameson A, 2011, Facilitating the Adoption of Unstructured High-Order Methods Amongst a Wider Community of Fluid Dynamicists, Mathematical Modelling of Natural Phenomena, Vol: 6, Pages: 97-140, ISSN: 0973-5348
Theoretical studies and numerical experiments suggest that unstructured high-order methods can provide solutions to otherwise intractable fluid flow problems within complex geometries. However, it remains the case that existing high-order schemes are generally less robust and more complex to implement than their low-order counterparts. These issues, in conjunction with difficulties generating high-order meshes, have limited the adoption of high-order techniques in both academia (where the use of low-order schemes remains widespread) and industry (where the use of low-order schemes is ubiquitous). In this short review, issues that have hitherto prevented the use of high-order methods amongst a non-specialist community are identified, and current efforts to overcome these issues are discussed. Attention is focused on four areas, namely the generation of unstructured high-order meshes, the development of simple and efficient time integration schemes, the development of robust and accurate shock capturing algorithms, and finally the development of high-order methods that are intuitive and simple to implement. With regards to this final area, particular attention is focused on the recently proposed flux reconstruction approach, which allows various well known high-order schemes (such as nodal discontinuous Galerkin methods and spectral difference methods) to be cast within a single unifying framework. It should be noted that due to the experience of the authors the review is directed somewhat towards aerodynamic applications and compressible flow. However, many of the discussions have a wider applicability. Moreover, the tone of the review is intended to be generally accessible, such that an extended scientific community can gain insight into factors currently pacing the adoption of unstructured high-order methods.
Vincent PE, Sherwin SJ, Weinberg PD, 2010, The Effect of the Endothelial Glycocalyx Layer on Concentration Polarisation of Low Density Lipoprotein in Arteries, Journal of Theoretical Biology, Vol: 265, Pages: 1-17, ISSN: 0022-5193
It has been postulated that a flow-dependent (and hence spatially varying) low density lipoprotein (LDL) concentration polarisation layer forms on the luminal surface of the vascular endothelium. Such a layer has the potential to cause heterogeneity in the distribution of atherosclerotic lesions by spatially modulating the rate of LDL transport into the arterial wall. Theoretical analysis suggests that a transmural water flux which is spatially heterogeneous at the cellular scale can act to enhance LDL concentration polarisation in a shear dependent fashion. However, such an effect is only observed if a relevant Peclet number (i.e. the ratio of LDL convection to LDL diffusion) is of order unity or greater. Based on the diffusivity of LDL in blood plasma, such a Peclet number is found to be far less than unity, implying that the aforementioned enhancement and shear dependence will not occur. However, this conclusion ignores the existence of the endothelial glycocalyx layer (EGL), which may inhibit the diffusion of LDL near the luminal surface of the endothelium, and hence raise any Peclet number associated with the transport of LDL. The present study numerically investigates the effect of the EGL, as well as a heterogeneous transmural water flux, on arterial LDL concentration polarisation. Particular attention is paid to measures of LDL concentration polarisation thought relevant to the rate of transendothelial LDL transport. It is demonstrated that an EGL is unlikely to cause any additional shear dependence of such measures directly, irrespective of whether or not LDL can penetrate into the EGL. However, it is found that such measures depend significantly on the nature of the interaction between LDL and the EGL (parameterised by the height of the EGL, the depth to which LDL penetrates into the EGL, and the diffusivity of LDL in the EGL). Various processes may regulate the interaction of LDL with the EGL, possibly in a flow dependent and hence spatially non-uniform f
Moore P, Barlis P, Spiro J, et al., 2009, A Randomized Optical Coherence Tomography Study of Coronary Stent Strut Coverage and Luminal Protrusion With Rapamycin-Eluting Stents, Journal of the American College of Cardiology Cardiovascular Interventions, Vol: 2, Pages: 437-444, ISSN: 1936-8798
Objectives We used optical coherence tomography, which has a resolution of <20 mu m, to analyze thin layers of neointima in rapamycin-eluting coronary stents.Background Lack of neointimal coverage has been implicated in the pathogenesis of drug-eluting coronary stent thrombosis. Angiography and intracoronary ultrasound lack the resolution to examine this.Methods We conducted a randomized trial in patients receiving polymer-coated rapamycin-eluting stents (Cypher, Cordis, Johnson & Johnson, Miami, Florida) and nonpolymer rapamycin-eluting stents (Yukon, Translumina, Hechingen, Germany) to examine neointimal thickness, stent strut coverage, and protrusion at 90 days. Twenty-four patients (n = 12 for each group) underwent stent deployment and invasive follow-up at 90 days with optical coherence tomography. The primary end point was binary stent strut coverage. Coprimary end points were neointimal thickness and stent strut luminal protrusion.Results No patient had angiographic restenosis. For polymer-coated and nonpolymer rapamycin-eluting stents, respectively, mean (SD), neointimal thickness was 77.2 (25.6) mu m versus 191.2 (86.7) mu m (p < 0.001). Binary stent strut coverage was 88.3% (11.8) versus 97.2% (6.1) (p = 0.030). Binary stent strut protrusion was 26.5% (17.5) versus 4.8% (8.6) (p = 0.001).Conclusions Mean neointimal thickness for the polymer-coated rapamycin-eluting stent was significantly less than the nonpolymer rapamycin-eluting stent but as a result coverage was not homogenous, with >10% of struts being uncovered. High-resolution imaging allowed development of the concept of the protrusion index, and >25% of struts protruded into the vessel lumen with the polymer-coated rapamycin-eluting stent compared with <5% with the nonpolymer rapamycin-eluting stent. These findings may have important implications for the risk of stent thrombosis and, therefore, future stent design. (An optical coherence tomography study to determine stent coverag
Vincent PE, Sherwin SJ, Weinberg PD, 2009, The Effect of a Spatially Heterogeneous Transmural Water Flux on Concentration Polarization of Low Density Lipoprotein in Arteries, Biophysical Journal, Vol: 96, Pages: 3102-3115, ISSN: 0006-3495
Uptake of low density lipoprotein (LDL) by the arterial wall is likely to play a key role in atherogenesis. A particular process that may cause vascular scale heterogeneity in the rate of transendothelial LDL transport is the formation of a flow-dependent LDL concentration polarization layer on the luminal surface of the arterial endothelium. In this study, the effect of a spatially heterogeneous transmural water flux (that traverses the endothelium only via interendothelial cell clefts) on such concentration polarization is investigated numerically. Unlike in previous investigations, realistic intercellular cleft dimensions are used here and several values of LDL diffusivity are considered. Particular attention is paid to the spatially averaged LDL concentration adjacent to different regions of the endothelial surface, as such measures may be relevant to the rate of transendothelial LDL transport. It is demonstrated in principle that a heterogeneous transmural water flux can act to enhance such measures, and cause them to develop a shear dependence (in addition to that caused by vascular scale flow features, affecting the overall degree of LDL concentration polarization). However, it is shown that this enhancement and additional shear dependence are likely to be negligible for a physiologically realistic transmural flux velocity of 0.0439 mu m s(-1) and an LDL diffusivity (in blood plasma) of 28.67 mu m(2) s(-1). Hence, the results imply that vascular scale studies of LDL concentration polarization are justified in ignoring the effect of a spatially heterogeneous transmural water flux.
Vincent PE, Hunt AAE, Grinberg L, et al., 2009, A Realistic Representation of the Rabbit Aorta for use in Computational Haemodynamic Studies, ASME Summer Bioengineering Conference, Publisher: AMER SOC MECHANICAL ENGINEERS, Pages: 985-986
Vincent P, 2009, A Cellular Scale Study of Low Denisty Lipoprotein Concentration Polarisation in Arteries
Uptake of Low Density Lipoprotein (LDL) by the arterial wall is likely to play a key role in the process of atherogenesis, which occurs non-uniformly within the ar- terial vasculature. A particular process that may cause vascular scale heterogeneity in the rate of transendothelial LDL transport is the formation of a flow-dependent LDL concentration polarisation layer adjacent to the luminal surface of the arte- rial endothelium. In this thesis the effects of cellular scale endothelial features on such LDL concentration polarisation are investigated using an idealised theoretical model. Specifically, the effect of a spatially heterogeneous transmural water flux is considered (flowing only through intercellular clefts), as well as the effect of the endothelial glycocalyx layer (EGL). The idealised model is implemented using both analytical techniques and the spectral/hp element method. A range of scenarios are considered, including those were no EGL is present, those where an EGL is present but LDL cannot penetrate into it, and finally those where an EGL is present and LDL can penetrate into it.For cases where no EGL is present, particular attention is paid to the spatially averaged LDL concentration adjacent to various regions of the endothelial surface, as such measures may be relevant to the rate of transendothelial LDL transport. It is demonstrated, in principle, that a heterogeneous transmural water flux alone can act to enhance such measures, and cause them to develop a shear dependence (in addition to that caused by vascular scale flow features affecting the overall degree of LDL concentration polarisation). However, it is shown that this enhancement and additional shear dependence are likely to be negligible for a physiologically realistictransmural flux velocity of 0.0439μms−1 and an LDL diffusivity in blood plasma of 28.67μm2 s−1 .For cases where an EGL is present, measures of LDL concentration polarisation relevant to the rate of transendo
Vincent PE, Sherwin SJ, Weinberg PD, 2008, Viscous Flow Over Outflow Slits Covered by an Anistropic Brinkman Medium: A Model of Flow Above Inter-Endothelial Cell Clefts, Physics of Fluids, Vol: 20
Vincent PE, Sherwin SJ, Weinberg PD, 2007, Computational investigation of a mechanism by which blood flow could control lipoprotein uptake by the arterial, Joint Autumn Meeting of the British-Society-for-Cardiovascular-Research/British-Atherosclerosis-Society, Publisher: B M J PUBLISHING GROUP, ISSN: 1355-6037
Chittenden JP, Vincent P, Jennings CA, et al., 2006, Hotspot ignition using a Z-pinch precursor plasma in a magneto-inertial ICF scheme, Publisher: American Institute of Physics, Pages: 335-338, ISSN: 0094-243X
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