Parallel finite element simulation of mooring forces on floating objects

The coupling between the equations governing the free‐surface flows, the six degrees of freedom non‐linear rigid body dynamics, the linear elasticity equations for mesh‐moving and the cables has resulted in a fluid‐structure interaction technology capable of simulating mooring forces on floating objects. The finite element solution strategy is based on a combination approach derived from fixed‐mesh and moving‐mesh techniques. Here, the free‐surface flow simulations are based on the Navier–Stokes equations written for two incompressible fluids where the impact of one fluid on the other one is extremely small. An interface function with two distinct values is used to locate the position of the free‐surface. The stabilized finite element formulations are written and integrated in an arbitrary Lagrangian–Eulerian domain. This allows us to handle the motion of the time dependent geometries. Forces and momentums exerted on the floating object by both water and hawsers are calculated and used to update the position of the floating object in time. In the mesh moving scheme, we assume that the computational domain is made of elastic materials. The linear elasticity equations are solved to obtain the displacements for each computational node. The non‐linear rigid body dynamics equations are coupled with the governing equations of fluid flow and are solved simultaneously to update the position of the floating object. The numerical examples includes a 3D simulation of water waves impacting on a moored floating box and a model boat and simulation of floating object under water constrained with a cable. Copyright © 2003 John Wiley & Sons, Ltd.     

Calculation of turbulent fluid flow and heat transfer in ducts by a full Reynolds stress model

A computational method has been developed to predict the turbulent Reynolds stresses and turbulent heat fluxes in ducts by different turbulence models. The turbulent Reynolds stresses and other turbulent flow quantities are predicted with a full Reynolds stress model (RSM). The turbulent heat fluxes are modelled by a SED concept, the GGDH and the WET methods. Two wall functions are used, one for the velocity field and one for the temperature field. All the models are implemented for an arbitrary three‐dimensional channel. Fully developed condition is achieved by imposing cyclic boundary conditions in the main flow direction. The numerical approach is based on the finite volume technique with a non‐staggered grid arrangement. The pressure–velocity coupling is handled by using the SIMPLEC‐algorithm. The convective terms are treated by the van Leer scheme while the diffusive terms are handled by the central‐difference scheme. The hybrid scheme is used for solving the ε equation. The secondary flow generation using the RSM model is compared with a non‐linear k–ε model (non‐linear eddy viscosity model). The overall comparison between the models is presented in terms of the friction factor and Nusselt number. Copyright © 2003 John Wiley & Sons, Ltd.     

A high‐fidelity low‐cost aerodynamic model using proper orthogonal decomposition

In this paper a high‐fidelity aerodynamic model is presented for use in parametric studies of weapon aerodynamics. The method employs a reduced‐order model obtained from the proper orthogonal decomposition (POD) of an ensemble of computational fluid dynamics (CFD) solutions with varying parameters. This decomposition produces an optimal linear set of orthogonal basis functions that best describe the ensemble of numerical solutions. These solutions are then projected onto this set of basis functions to provide a finite set of scalar coefficients that represent the solutions. A pseudo‐continuous representation of these projection coefficients is constructed, which allows predictions to be made of parameter combinations not in the original set of observations. The paper explores the performance of a few design‐of‐experiment approaches for the generation of the initial ensemble of computational experiments. Response surface construction methods based on parametric and non‐parametric models for the pseudo‐continuous representation of the projection coefficients are also evaluated. The model has been applied to two‐flow problems related to high‐speed weapon aerodynamics, inviscid flow around a flare‐stabilized hypersonic projectile and supersonic turbulent flow around a fin‐stabilized projectile with drooping nose control. Comparisons of model predictions with high‐fidelity CFD simulations suggest that the POD provides a reliable and robust approach to the construction of reduced‐order models. The practicality of the model is shown to be sensitive to the technique used to generate the ensemble of observations from which the model is constructed, while the accuracy of the approach depends on the pseudo‐continuous representation of the projection coefficients. Copyright © 2009 John Wiley & Sons, Ltd.     

A novel efficient hybrid DSMC–dynamic collision limiter algorithm for multiscale transitional flows

A new 2D parallel multispecies polyatomic particle–based hybrid flow solver is developed by coupling the Direct Simulation Monte Carlo (DSMC) method with a novel Dynamic Collision Limiter (DCL) approach to solve multiscale transitional flows. The hybrid DSMC‐DCL solver can solve nonequilibrium multiscale flows with length scales ranging from continuum to rarefied. The DCL method, developed in this work, dynamically assigns different number of collisions in cells, which is based on the local value of K‐S parameter such that the number of collisions per time step is limited in near‐equilibrium flow regions. Present hybrid solver uses the Kolmogorov‐Smirnov statistical test as the continuum breakdown parameter, based on which, the solution domain is decomposed into near‐equilibrium and nonequilibrium flow regions. Direct Simulation Monte Carlo is used where nonequilibrium flow regions are encountered, while the DCL method is used where flow regions are found to be in near‐equilibrium state. In this work, we have studied hypersonic flow of nitrogen over a blunt body with an aerospike and supersonic flow of argon through a micronozzle. The results obtained by the hybrid DSMC‐DCL solver are compared and shown to agree well with the experimental data and with those obtained from DSMC, with significant savings in the computational cost.     

Time‐dependent turbulent cavitating flow computations with interfacial transport and filter‐based models

Turbulent cavitating flow computations need to address both cavitation and turbulence modelling issues. A recently developed interfacial dynamics‐based cavitation model (IDCM) incorporates the interfacial transport into the computational modelling of cavitation dynamics. For time‐dependent flows, it is known that the engineering turbulence closure such as the original k–ε model often over‐predicts the eddy viscosity values reducing the unsteadiness. A recently proposed filter‐based modification has shown that it can effectively modulate the eddy viscosity, rendering better simulation capabilities for time‐dependent flow computations in term of the unsteady characteristics. In the present study, the IDCM along with the filter‐based k–ε turbulence model is adopted to simulate 2‐D cavitating flows over the Clark‐Y airfoil. The chord Reynolds number is Re=7.0 × 10⁵. Two angles‐of‐attack of 5 and 8° associated with several cavitation numbers covering different flow regimes are conducted. The simulation results are assessed with the experimental data including lift, drag and velocity profiles. The interplay between cavitation and turbulence models reveals substantial differences in time‐dependent flow results even though the time‐averaged characteristics are similar. Copyright © 2005 John Wiley & Sons, Ltd.     

Blood flow dynamics and fluid–structure interaction in patient‐specific bifurcating cerebral aneurysms

Hemodynamics plays an important role in the progression and rupture of cerebral aneurysms. The current work describes the blood flow dynamics and fluid–structure interaction in seven patient‐specific models of bifurcating cerebral aneurysms located in the anterior and posterior circulation regions of the circle of Willis. The models were obtained from 3D rotational angiography image data, and blood flow dynamics and fluid–structure interaction were studied under physiologically representative waveform of inflow. The arterial wall was assumed to be elastic, isotropic and homogeneous. The flow was assumed to be laminar, non‐Newtonian and incompressible. In one case, the effects of different model suppositions and boundary conditions were reported in detail. The fully coupled fluid and structure models were solved with the finite elements package ADINA. The vortex structure, pressure, wall shear stress (WSS), effective stress and displacement of the aneurysm wall showed large variations, depending on the morphology of the artery, aneurysm size and position. The time‐averaged WSS, effective stress and displacement at the aneurysm fundus vary between 0.17 and 4.86 Pa, 4.35 and 170.2 kPa and 0.16 and 0.74 mm, respectively, for the seven patient‐specific models of bifurcating cerebral aneurysms. Copyright © 2008 John Wiley & Sons, Ltd.     

An algebraic variational multiscale–multigrid method for large‐eddy simulation of turbulent pulsatile flows in complex geometries with detailed insight into pulmonary airway flow

The algebraic variational multiscale–multigrid method, an advanced computational approach recently proposed for large‐eddy simulation of turbulent flow, is further developed in this study for turbulent flow simulations in complex geometries. In particular, it is applied to the complex case of pulsatile turbulent flow dynamics of the upper and lower pulmonary airways up to generation 7 and carefully investigated for this important application. Among other things, the results obtained with the proposed method are compared with the results obtained with a rather traditional stabilized finite element method. As opposed to previous large‐eddy simulations of pulmonary airways, we consider a pulsatile inflow condition, allowing the development of turbulence over a pulse cycle to be investigated, which obviously makes these results more physiologically realistic. Our results suggest that turbulent effects in the bronchial airways are rather weak and can completely decay as early as the third generation, depending on geometry and flow distribution. Both methods utilized in this study are able to adequately capture all flow stages from laminar via transitional to turbulent regimes without any modifications. However, the algebraic variational multiscale–multigrid method provides superior results as soon as the flow enters the most challenging, turbulent flow regime. Furthermore, the robustness of the scale‐separation approach based on plain aggregation algebraic multigrid inherent to the algebraic variational multiscale–multigrid method is demonstrated for the present complex geometry. Copyright © 2012 John Wiley & Sons, Ltd.     

Multiscale coupling of molecular dynamics and peridynamics

We propose a multiscale computational model to couple molecular dynamics and peridynamics. The multiscale coupling model is based on a previously developed multiscale micromorphic molecular dynamics (MMMD) theory, which has three dynamics equations at three different scales, namely, microscale, mesoscale, and macroscale. In the proposed multiscale coupling approach, we divide the simulation domain into atomistic region and macroscale region. Molecular dynamics is used to simulate atom motions in atomistic region, and peridynamics is used to simulate macroscale material point motions in macroscale region, and both methods are nonlocal particle methods. A transition zone is introduced as a messenger to pass the information between the two regions or scales. We employ the “supercell” developed in the MMMD theory as the transition element, which is named as the adaptive multiscale element due to its ability of passing information from different scales, because the adaptive multiscale element can realize both top-down and bottom-up communications. We introduce the Cauchy–Born rule based stress evaluation into state-based peridynamics formulation to formulate atomistic-enriched constitutive relations. To mitigate the issue of wave reflection on the interface, a filter is constructed by switching on and off the MMMD dynamic equations at different scales. Benchmark tests of one-dimensional (1-D) and two-dimensional (2-D) wave propagations from atomistic region to macro region are presented. The mechanical wave can transit through the interface smoothly without spurious wave deflections, and the filtering process is proven to be efficient.     

A comparative study of two fast nonlinear free‐surface water wave models

This paper presents a comparison in terms of accuracy and efficiency between two fully nonlinear potential flow solvers for the solution of gravity wave propagation. One model is based on the high‐order spectral (HOS) method, whereas the second model is the high‐order finite difference model OceanWave3D. Although both models solve the nonlinear potential flow problem, they make use of two different approaches. The HOS model uses a modal expansion in the vertical direction to collapse the numerical solution to the two‐dimensional horizontal plane. On the other hand, the finite difference model simply directly solves the three‐dimensional problem. Both models have been well validated on standard test cases and shown to exhibit attractive convergence properties and an optimal scaling of the computational effort with increasing problem size. These two models are compared for solution of a typical problem: propagation of highly nonlinear periodic waves on a finite constant‐depth domain. The HOS model is found to be more efficient than OceanWave3D with a difference dependent on the level of accuracy needed as well as the wave steepness. Also, the higher the order of the finite difference schemes used in OceanWave3D, the closer the results come to the HOS model. Copyright © 2011 John Wiley & Sons, Ltd.     

Multidimensional modeling of the stenosed carotid artery: A novel CAD approach accompanied by an extensive lumped model

This study describes a multidimensional 3D/lumped parameter(LP) model which contains appropriate inflow/outflow boundary conditions in order to model the entire human arterial trees. A new extensive LP model of the entire arterial network(48 arteries) was developed including the effect of vessel diameter tapering and the parameterization of resistance, conductor and inductor variables. A computer aided-design(CAD) algorithm was proposed to effciently handle the coupling of two or more 3D models with the LP model, and substantially lessen the coupling processing time. Realistic boundary conditions and Navier–Stokes equations in healthy and stenosed models of carotid artery bifurcation(CAB) were used to investigate the unsteady Newtonian blood flow velocity distribution in the internal carotid artery(ICA). The present simulation results agree well with previous experimental and numerical studies. The outcomes of a pure LP model and those of the coupled 3D healthy model were found to be nearly the same in both cases. Concerning the various analyzed 3D zones, the stenosis growth in the ICA was not found as a crucial factor in determining the absorbing boundary conditions.This paper demonstrates the advantages of coupling local and systemic models to comprehend physiological diseases of the cardiovascular system.     

Computational modelling of variably saturated flow in porous media with complex three‐dimensional geometries

A computational procedure is presented for solving complex variably saturated flows in porous media, that may easily be implemented into existing conventional finite‐volume‐based computational fluid dynamics codes, so that their functionality might be geared upon to readily enable the modelling of a complex suite of interacting fluid, thermal and chemical reaction process physics. This procedure has been integrated within a multi‐physics finite volume unstructured mesh framework, allowing arbitrarily complex three‐dimensional geometries to be modelled. The model is particularly targeted at ore heap‐leaching processes, which encounter complex flow problems, such as infiltration into dry soil, drainage, perched water tables and flow through heterogeneous materials, but is equally applicable to any process involving flow through porous media, such as in environmental recovery processes. The computational procedure is based on the mixed form of the classical Richards equation, employing an adaptive transformed mixed algorithm that is numerically robust and significantly reduces compute (or CPU) time. The computational procedure is accurate (compares well with other methods and analytical data), comprehensive (representing any kind of porous flow model), and is computationally efficient. As such, this procedure provides a suitable basis for the implementation of large‐scale industrial heap‐leach models. Copyright © 2005 John Wiley & Sons, Ltd.     

Non‐Newtonian blood flow study in a model cavopulmonary vascular system

A transient haemodynamic study in a model cavopulmonary vascular system has been carried out for a typical range of parameters using a finite element‐based Navier–Stokes solver. The focus of this study is to investigate the influence of non‐Newtonian behaviour of the blood on the haemodynamic quantities, such as wall shear stress (WSS) and flow pattern. The computational fluid dynamics (CFD) model is based on an artificial compressibility characteristic‐based split (AC‐CBS) scheme, which has been adopted to solve the Navier–Stokes equations in space–time domain. A power law model has been implemented to characterize the shear thinning nature of the blood depending on the local strain rate. Using the computational model, numerical investigations have been performed for Newtonian and non‐Newtonian flows for different frequencies and input pulse forms. The haemodynamic quantities observed in total cavopulmonary connection (TCPC) for the above conditions suggest that there are considerable differences in average (about 25–40%) and peak (about 50%) WSS distributions, when the non‐Newtonian behaviour of the blood is taken into account. The lower WSS levels observed for non‐Newtonian cases point to the higher risk of lesion formation, especially at higher pulsation frequencies. A realistic pulse form is relatively safer than a sinusoidal pulse as it has more energy distributed in the higher harmonics, which results in higher average WSS values. The present study highlights the importance of including non‐Newtonian shear thinning behaviour for modelling blood flow in the vicinity of repaired arterial connections. Copyright © 2010 John Wiley & Sons, Ltd.     

A depth‐integrated non‐hydrostatic finite element model for wave propagation

This paper presents a two‐dimensional finite element model for simulating dynamic propagation of weakly dispersive waves. Shallow water equations including extra non‐hydrostatic pressure terms and a depth‐integrated vertical momentum equation are solved with linear distributions assumed in the vertical direction for the non‐hydrostatic pressure and the vertical velocity. The model is developed based on the platform of a finite element model, CCHE2D. A physically bounded upwind scheme for the advection term discretization is developed, and the quasi second‐order differential operators of this scheme result in no oscillation and little numerical diffusion. The depth‐integrated non‐hydrostatic wave model is solved semi‐implicitly: the provisional flow velocity is first implicitly solved using the shallow water equations; the non‐hydrostatic pressure, which is implicitly obtained by ensuring a divergence‐free velocity field, is used to correct the provisional velocity, and finally the depth‐integrated continuity equation is explicitly solved to satisfy global mass conservation. The developed wave model is verified by an analytical solution and validated by laboratory experiments, and the computed results show that the wave model can properly handle linear and nonlinear dispersive waves, wave shoaling, diffraction, refraction and focusing. Copyright © 2013 John Wiley & Sons, Ltd.     

Unstructured lattice Boltzmann method in three dimensions

Over the last decade, the lattice Boltzmann method (LBM) has evolved into a valuable alternative to continuum computational fluid dynamics (CFD) methods for the numerical simulation of several complex fluid‐dynamic problems. Recent advances in lattice Boltzmann research have considerably extended the capability of LBM to handle complex geometries. Among these, a particularly remarkable option is represented by cell‐vertex finite‐volume formulations which permit LBM to operate on fully unstructured grids. The two‐dimensional implementation of unstructured LBM, based on the use of triangular elements, has shown capability of tolerating significant grid distortions without suffering any appreciable numerical viscosity effects, to second‐order in the mesh size. In this work, we present the first three‐dimensional generalization of the unstructured lattice Boltzmann technique (ULBE as unstructured lattice Boltzmann equation), in which geometrical flexibility is achieved by coarse‐graining the lattice Boltzmann equation in differential form, using tetrahedrical grids. This 3D extension is demonstrated for the case of 3D pipe flow and moderate Reynolds numbers flow past a sphere. The results provide evidence that the ULBE has significant potential for the accurate calculation of flows in complex 3D geometries. Copyright © 2005 John Wiley & Sons, Ltd.     

基于规则网络的碳酸盐岩多尺度网络模型构建方法研究

碳酸盐岩油藏非均质性强,孔隙大小变化可达好几个数量级,描述碳酸盐岩油藏多尺度孔隙特征具有重要意义.本文首先基于三维规则网络模型建立了不同物理尺寸的溶洞网络、大孔隙网络和微孔隙网络;然后提出一种耦合算法,以溶洞网络为基础,通过添加适当比例的大孔隙和微孔隙,构建出碳酸盐岩多尺度网络模型;最后对比分析了各网络模型的几何性质、拓扑性质和绝对渗透率.结果表明,碳酸盐岩多尺度网络模型能够同时描述不同尺度孔隙的几何和拓扑特征;且相比各单一尺度的孔隙网络模型,多尺度网络模型有着较高的绝对渗透率,这是由于各尺度孔隙之间的相互连通极大地提高了网络的整体连通性和流动能力,为碳酸盐岩油藏微观渗流模拟提供了重要的研究平台.     

Flow effects of blood constitutive equations in 3D models of vascular anomalies

The effects of different blood rheological models are investigated numerically utilizing two three‐ dimensional (3D) models of vascular anomalies, namely a stenosis and an abdominal aortic aneurysm model. The employed CFD code incorporates the SIMPLE scheme in conjunction with the finite‐volume method with collocated arrangement of variables. The approximation of the convection terms is carried out using the QUICK differencing scheme, whereas the code enables also multi‐block computations, which are useful in order to cope with the two‐block grid structure of the current computational domain. Three non‐Newtonian models are employed, namely the Casson, Power‐Law and Quemada models, which have been introduced in the past for modelling the rheological behaviour of blood and cover both the viscous as well as the two‐phase character of blood. In view of the haemodynamical mechanisms related to abnormalities in the vascular network and the role of the wall shear stress in initiating and further developing of arterial diseases, the present study focuses on the 3D flow field and in particular on the distribution as well as on both low and high values of the wall shear stress in the vicinity of the anomaly. Finally, a comparison is made between the effects of each rheological model on the aforementioned parameters. Results show marked differences between simulating blood as Newtonian and non‐Newtonian fluid and furthermore the Power‐Law model exhibits different behaviour in all cases compared to the other models whereas Quemada and Casson models exhibit similar behaviour in the case of the stenosis but different behaviour in the case of the aneurysm. Copyright © 2005 John Wiley & Sons, Ltd.     

Multiscale tow-phase flow modeling of sheet and cloud cavitation

A multiscale two-phase flow model based on a coupled Eulerian/Lagrangian approach is applied to capture the sheet cavitation formation, development, unsteady breakup, and bubble cloud shedding on a hydrofoil. No assumptions are needed on mass transfer. Instead natural free field nuclei and solid boundary nucleation are modelled and enable capture of the sheet and cloud dynamics. The multiscale model includes a micro-scale model for tracking the bubbles, a macro-scale model for describing large cavity dynamics, and a transition scheme to bridge the micro and macro scales. With this multiscale model small nuclei are seen to grow into large bubbles, which eventually merge to form a large scale sheet cavity. A reentrant jet forms under the sheet cavity, travels upstream, and breaks the cavity, resulting in the emission of high pressure peaks as the broken pockets shrink and collapse while travelling downstream. The method is validated on a 2D NACA0015 foil and is shown to be in good agreement with published experimental measurements in terms of sheet cavity lengths and shedding frequencies. Sensitivity assessment of the model parameters and 3D effects on the predicted major cavity dynamics are also discussed.