Correction to: Impact of leg bending in the patient-specific computational fluid dynamics of popliteal stenting

Acta Mechanica Sinica - A Correction to this paper has been published: https://doi.org/10.1007/s10409-021-01066-2     

Expectations for computational fluid dynamics

This article presents a sampling of the author's expectations for the field of computational fluid dynamics (CFD) in the areas of research, development and application. The primary focus of the discussion herein is related to the non-linear transonic flow regime, and more specifically, for calculations about commercial transport aircraft. However, many of these topics are pertinent to all flow field regimes and aircraft designs. The underlying goal is to enable the automation of multi-disciplinary design processes, which utilize state-of-the-art numerical simulation methods. These include issues pertaining to accuracy, robustness, efficiency, ease-of-use, uncertainty requirements and other challenges.     

Domain decomposition methods in computational fluid dynamics

The divide-and-conquer paradigm of iterative domain decomposition or substructuring has become a practical tool in computational fluid dynamics applications because of its flexibility in accommodating adaptive refinement through locally uniform (or quasi-uniform) grids, its ability to exploit multiple discretizations of the operator equations, and the modular pathway it provides towards parallelism. We illustrate these features on the classic model problem of flow over a backstep using Newton's method as the non-linear iteration. Multiple discretizations (second-order in the operator and first-order in the preconditioner) and locally uniform mesh refinement pay dividends separately and can be combined synergistically. We include sample performance results from an Intel iPSC/860 hypercube implementation.     

Direct modeling for computational fluid dynamics

All fluid dynamic equations are valid under their modeling scales, such as the particle mean free path and mean collision time scale of the Boltzmann equation and the hydrodynamic scale of the Navier–Stokes(NS) equations.The current computational fluid dynamics(CFD) focuses on the numerical solution of partial differential equations(PDEs), and its aim is to get the accurate solution of these governing equations. Under such a CFD practice, it is hard to develop a unified scheme that covers flow physics from kinetic to hydrodynamic scales continuously because there is no such governing equation which could make a smooth transition from the Boltzmann to the NS modeling. The study of fluid dynamics needs to go beyond the traditional numerical partial differential equations. The emerging engineering applications, such as air-vehicle design for near-space flight and flow and heat transfer in micro-devices, do require further expansion of the concept of gas dynamics to a larger domain of physical reality, rather than the traditional distinguishable governing equations. At the current stage, the non-equilibrium flow physics has not yet been well explored or clearly understood due to the lack of appropriate tools.Unfortunately, under the current numerical PDE approach, it is hard to develop such a meaningful tool due to the absence of valid PDEs. In order to construct multiscale and multiphysics simulation methods similar to the modeling process of constructing the Boltzmann or the NS governing equations, the development of a numerical algorithm should be based on the first principle of physical modeling. In this paper, instead of following the traditional numerical PDE path, we introduce direct modeling as a principle for CFD algorithm development. Since all computations are conducted in a discretized space with limited cell resolution, the flow physics to be modeled has to be done in the mesh size and time step scales.Here, the CFD is more or less a direct construction of discrete numerical evolution equations, where the mesh size and time step will play dynamic roles in the modeling process.With the variation of the ratio between mesh size and local particle mean free path, the scheme will capture flow physics from the kinetic particle transport and collision to the hydrodynamic wave propagation. Based on the direct modeling, a continuous dynamics of flow motion will be captured in the unified gas-kinetic scheme. This scheme can be faithfully used to study the unexplored non-equilibrium flow physics in the transition regime.     

Understanding coherent vortices through computational fluid dynamics

A new definition of coherent vortices in turbulence is proposed, where the vorticity equation reduces to a cyclostrophic balance. Afterward, we describe five fundamental vortex interactions, the sheet, the spiral, the pairing, the even longitudinal, and the odd longitudinal modes. Numerous examples of these interactions are provided from direct numerical or large-eddy simulations. The resulting vortices are responsible for the internal intermittent character of turbulence, with highly nongaussian tails for the probability density functions of vorticity, passive scalar, and low pressure. In a mixing layer, the combination of the odd longitudinal and the pairing modes (helical pairing) is inhibited by compressibility, above a convective Mach number of 0.7. When turbulence is submitted to a solid-body rotation, anticyclonic vortices of local Rossby number of the order of 1 transform into intense perpendicular Görtler-type alternate longitudinal vortices.The support of CCVR, CEA, CNRS, Dassault/CNES, DRET, LHF, and Région Rhône-Alpes is acknowledged. This paper is the text of an invited lecture given at the IUTAM Symposium on Eddy Structure Identification in Free Turbulent Shear Flows, Poitiers, 12–14 October 1992.     

Exploring alternative approaches to computational fluid dynamics

This paper discusses advances in two areas which may have the potential to impact future simulation capabilities through advanced algorithms. This includes spectral multigrid (MG) solvers for high-order accurate spatial discretizations and efficient MG solvers for kinetic-based schemes. Preliminiary evidence is given illustrating the promise of these approaches for application to engineering simulations.     

Large-scale computational fluid dynamics by the finite element method

Solution methods are presented for the large systems of linear equations resulting from the implicit, coupled solution of the Navier-Stokes equations in three dimensions. Two classes of methods for such solution have been studied: direct and iterative methods. For direct methods, sparse matrix algorithms have been investigated and a Gauss elimination, optimized for vector-parallel processing, has been developed. Sparse matrix results indicate that reordering algorithms deteriorate for rectangular, i.e. M × M × N, grids in three dimensions as N gets larger than M. A new local nested dissection reordering scheme that does not suffer from these difficulties, at least in two dimensions, is presented. The vector-parallel Gauss elimination is very efficient for processing on today's supercomputers, achieving execution rates exceeding 2.3 Gflops the Cray YMP-8 and 9.2 Gflops on the NEC on SX3. For iterative methods, two approaches are developed. First, conjugate-gradient-like methods are studied and good results are achieved with a preconditioned conjugate gradient squared algorithm. Convergence of such a method being sensitive to the preconditioning, a hybrid viscosity method is adopted whereby the preconditioner has an artificial viscosity that is gradually lowered, but frozen at a level higher than the dissipation introduced in the physical equations. The second approach is a domain decomposition one in which overlapping domain and side-by-side methods are tested. For the latter, a Lagrange multiplier technique achieves reasonable rates of convergence.     

Aircraft T-tail flutter predictions using computational fluid dynamics

The paper presents the application of computational aeroelasticity (CA) methods to the analysis of a T-tail stability in transonic regime. For this flow condition unsteady aerodynamics show a significant dependency from the aircraft equilibrium flight configuration, which rules both the position of shock waves in the flow field and the load distribution on the horizontal tail plane. Both these elements have an influence on the aerodynamic forces, and so on the aeroelastic stability of the system. The numerical procedure proposed allows to investigate flutter stability for a free-flying aircraft, iterating until convergence the following sequence of sub-problems: search for the trimmed condition for the deformable aircraft; linearize the system about the stated equilibrium point; predict the aeroelastic stability boundaries using the inferred linear model. An innovative approach based on sliding meshes allows to represent the changes of the computational fluid domain due to the motion of control surfaces used to trim the aircraft. To highlight the importance of keeping the linear model always aligned to the trim condition, and at the same time the capabilities of the computational fluid dynamics approach, the method is applied to a real aircraft with a T-tail configuration: the P180.     

Patient-specific finite element analysis of popliteal stenting

Nitinol self-expanding stents are used for the endovascular management of peripheral artery diseases of the popliteal artery, which is located behind the knee joint. Unfortunately, the complex kinematics of the artery during the leg flexion leads to severe loading conditions, favouring the mechanical failure of the stent, calling for a specific biomechanical analysis. For this reason, in the present study we reconstruct by medical image analysis the patient-specific popliteal kinematics during leg flexion, which is subsequently exploited to compute the mechanical response of a stent model, virtually implanted in the artery by structural finite element analysis (FEA). The medical image analysis indicates a non-uniform configuration change of the artery during the leg flexion, leading to an increase of the vessel curvature above the knee. The computed mechanical response of the stent reflects the non-uniform configuration change of the artery as after the flexion the average stress is higher in the part of the stent located above the knee. Although the proposed analysis is limited to a case-study, it shows the capability of patient-specific FEA simulations to compute the mechanical response of a stent model subjected to the complex and severe loading conditions of the popliteal artery during leg flexion.     

An implicit meshless method for application in computational fluid dynamics

An implicit meshless scheme is developed for solving the Euler equations, as well as the laminar and Reynolds‐averaged Navier–Stokes equations. Spatial derivatives are approximated using a least squares method on clouds of points. The system of equations is linearised, and solved implicitly using approximate, analytical Jacobian matrices and a preconditioned Krylov subspace iterative method. The details of the spatial discretisation, linear solver and construction of the Jacobian matrix are discussed; and results that demonstrate the performance of the scheme are presented for steady and unsteady two dimensional fluid flows. Copyright © 2012 John Wiley & Sons, Ltd.     

Multiresolution reproducing kernel particle method for computational fluid dynamics

Multiresolution analysis based on the reproducing kernel particle method (RKPM) is developed for computational fluid dynamics. An algorithm incorporating multiple-scale adaptive refinement is introduced. The concept of using a wavelet solution as an error indicator is also presented. A few representative numerical examples are solved to illustrate the performance of this new meshless method. Results show that the RKPM is a good candidate for tackling the widespread large-scale problems in fluid dynamics. © 1997 John Wiley & Sons, Ltd.     

A brief survey on discontinuous Galerkin methods in computational fluid dynamics

间断Galerkin （DG）方法结合了有限元法（具有弱形式、有限维解和试验函数空间）和有限体积法（具有数值通量、非线性限制器）的优点,特别适合对流占优问题（如激波等线性和非线性波）的模拟研究,本文述评DG 方法,强调其在计算流体力学（CFD）中的应用,文中讨论了DG 方法的必要构成要素和性能特点,并介绍了该方法的一些最近研究进展,相关工作促进了DG 方法在CFD 领域的应用,     

Multifield computational fluid dynamics model of particulate flow in curved circular tubes

Limitations of mass transfer resulting from non-optimized fluid mechanics can severely affect the performance of synthetic membrane filtration systems. To improve membrane efficiency, modern applications of this technology have extensively used curved membrane ducts that take advantage of Dean vortices (i.e., curvature-induced secondary flows) to minimize membrane fouling. This paper is concerned with a complete three-dimensional analysis of single-phase and two-phase particle/liquid flows around a curved membrane tube. The proposed multidimensional model was implemented in an advanced (next-generation) multiphase computational fluid dynamics (CFD) solver, NPHASE. The results of simulations have been validated against experimental data and compared against other findings available in the literature. The consistency and accuracy of the present approach have been demonstrated. The novel aspects of this work include: the demonstration that azimuthal vortices may bifurcate at Dean numbers lower than previously anticipated, the use of vorticity magnitude as a measure of vortex strength, and the explanation of the role that Dean vortices play to mitigate the effect of gravity on particle settling. The overall results have direct relevance to synthetic membrane fouling during filtration of particle suspensions.     

The computational fluid dynamics modelling of the autorotation of square,flat plates

This paper examines the use of a coupled Computational Fluid Dynamics (CFD) – Rigid Body Dynamics (RBD) model to study the fixed-axis autorotation of a square flat plate. The calibration of the model against existing wind tunnel data is described. During the calibration, the CFD models were able to identify complex period autoration rates, which were attributable to a mass eccentricity in the experimental plate. The predicted flow fields around the autorotating plates are found to be consistent with existing observations. In addition, the pressure coefficients from the wind tunnel and computational work were found to be in good agreement. By comparing these pressure distributions and the vortex shedding patterns at various stages through an autorotation cycle, it was possible to gain important insights into the flow structures that evolve around the plate. The CFD model is also compared against existing correlation functions that relate the mean tip speed ratio of the plate to the aspect ratio, thickness ratio and mass moment of inertia of the plate. Agreement is found to be good for aspect ratios of 1, but poor away from this value. However, other aspects of the numerical modelling are consistent with the correlations.     

A simulated annealing-based inverse computational fluid dynamics model for unknown parameter estimation in fluid flow problem

In this paper, a simulated annealing (SA)-based optimisation is carried out for simultaneous estimation of the Reynolds number (Re) and the dimensions of the enclosure (l_x, l_y ) from the knowledge of centreline velocity field. For demonstrating the retrieval methodology, the required centreline velocity field is first obtained from a forward method using some known values of the unknowns, which are ultimately estimated by the inverse method. SA is used to optimise the objective function represented by the square of the difference between the known field and an arbitrary guessed field (calculated using some guessed value of the unknowns). For studying the sensitivity of the estimated parameters, the effect of random errors has been investigated and the suitability of the SA has been checked for different initial guesses. The algorithm reported in the present work is useful in estimating the above unknowns (Re, l_x, l_y ) for a given velocity field.     

On Taylor weak statement finite element methods for computational fluid dynamics

A Taylor series augmentation of a weak statement (a ‘Taylor weak statement’ or ‘Taylor-Galerkin’ method) is used to systematically reduce the dispersion error in a finite element approximation of the one-dimensional transient advection equation. A frequency analysis is applied to determine the phase velocity of semi-implicit linear, quadratic and cubic basis one-dimensional finite element methods and of several comparative finite difference/finite volume algorithms. The finite element methods analysed include both Galerkin and Taylor weak statements. The frequency analysis is used to obtain an improved linear basis Taylor weak statement finite element algorithm. Solutions are reported for verification problems in one and two dimensions and are compared with finite volume solutions. The improved finite element algorithms have sufficient phase accuracy to achieve highly accurate linear transient solutions with little or no artificial diffusion.     

Erosion of oil&gas industry choke valves using computational fluid dynamics and experiment

As part of several years research activity with erosion in chokes, Norsk Hydro ASA has developed a model to estimate erosion and lifetime of chokes by incorporating erosion models into particulate flow models. This model has been verified with the results from flow and erosion testing of two different types of chokes, Needle&Seat and External Sleeve. The erosion tests with both the modified Needle&Seat choke and the External Sleeve choke gave peak erosion rates only two or three times larger than calculated. This is assumed to be near the uncertainty of the erosion model alone. This is very satisfactory for such complex flow geometries. The model and the experiments demonstrated that the External Sleeve choke is much more prone to erosion attack, at the given low pressure conditions.     

A study of autonomous underwater vehicle hull forms using computational fluid dynamics

Reduction of the propulsive power requirement by efficient hull form design is one of the important requirements for the successful operation of autonomous underwater vehicles (AUVs). In the absence of reliable and sufficiently accurate experimental data this will require experimental analysis of a large number of hull forms, a task which is both expensive and time-consuming. Recent developments in computational fluid dynamics (CFD) can offer a cost-effective solution to this problem. In this paper such a method is developed to simulate the flow past axisymmetric AUVs. Its application is discussed for four different hull forms. © 1997 John Wiley & Sons, Ltd.