A 3‐D non‐hydrostatic pressure model for small amplitude free surface flows

A three‐dimensional, non‐hydrostatic pressure, numerical model with k–ε equations for small amplitude free surface flows is presented. By decomposing the pressure into hydrostatic and non‐hydrostatic parts, the numerical model uses an integrated time step with two fractional steps. In the first fractional step the momentum equations are solved without the non‐hydrostatic pressure term, using Newton's method in conjunction with the generalized minimal residual (GMRES) method so that most terms can be solved implicitly. This method only needs the product of a Jacobian matrix and a vector rather than the Jacobian matrix itself, limiting the amount of storage and significantly decreasing the overall computational time required. In the second step the pressure–Poisson equation is solved iteratively with a preconditioned linear GMRES method. It is shown that preconditioning reduces the central processing unit (CPU) time dramatically. In order to prevent pressure oscillations which may arise in collocated grid arrangements, transformed velocities are defined at cell faces by interpolating velocities at grid nodes. After the new pressure field is obtained, the intermediate velocities, which are calculated from the previous fractional step, are updated. The newly developed model is verified against analytical solutions, published results, and experimental data, with excellent agreement. Copyright © 2005 John Wiley & Sons, Ltd.     

A 3D smoothed particle hydrodynamics model for erosional dam-break floods

A mesh-less smoothed particle hydrodynamics (SPH) model for bed-load transport on erosional dam-break floods is presented. This mixture model describes both the liquid phase and the solid granular material. The model is validated on the results from several experiments on erosional dam breaks. A comparison between the present model and a 2-phase SPH model for geotechnical applications (Gadget Soil; TUHH) is performed. A demonstrative 3D erosional dam break on complex topography is investigated. The present 3D mixture model is characterised by: no tuning parameter for the mixture viscosity; consistency with the Kinetic Theory of Granular Flow; ability to reproduce the evolution of the free surface and the bed-load transport layer; applicability to practical problems in civil engineering. The numerical developments of this study are represented by a new SPH scheme for bed-load transport, which is implemented in the SPH code SPHERA v.8.0 (RSE SpA), distributed as FOSS on GitHub.     

A new fully non‐hydrostatic 3D free surface flow model for water wave motions

A new fully non‐hydrostatic model is presented by simulating three‐dimensional free surface flow on a vertical boundary‐fitted coordinate system. A projection method, known as pressure correction technique, is employed to solve the incompressible Euler equations. A new grid arrangement is proposed under a horizontal Cartesian grid framework and vertical boundary‐fitted coordinate system. The resulting model is relatively simple. Moreover, the discretized Poisson equation for pressure correction is symmetric and positive definite, and thus it can be solved effectively by the preconditioned conjugate gradient method. Several test cases of surface wave motion are used to demonstrate the capabilities and numerical stability of the model. Comparisons between numerical results and analytical or experimental data are presented. It is shown that the proposed model could accurately and effectively resolve the motion of short waves with only two layers, where wave shoaling, nonlinearity, dispersion, refraction, and diffraction phenomena occur. Copyright © 2010 John Wiley & Sons, Ltd.     

三维编织复合材料渐进损伤的非线性模型及强度分析

建立了考虑周期性位移边界条件的细观体胞模型,对三维编织复合材料的渐进损伤过程进行数值模拟。采用Eshelby-Mori—Tanaka方法计算含损伤裂纹的材料的剐度矩阵,并将有限元网格尺寸和单元裂纹尺寸引入损伤演化方程,有效地降低了模拟结果对有限元网格的依赖程度。通过计算得到了材料应力应变的非线性关系和失效时的极限强度,并分析了材料的破坏机理。结果表明,大编织角材料的破坏模式主要是基体失效与纤维横向拉剪破坏,模拟计算结果与文献中的实验值吻合较好。     

A discrete 3D model for bridge aerodynamics and aeroelasticity: nonlinearities and linearizations

A framework for the numerical analysis of bridges under wind excitation is outlined. It is based on structural finite element scheme and cross-sectional wind load models. Two aspects are investigated: (1) how considering the mean steady configuration in the aerodynamic stability calculation; and (2) the effects of load nonlinearities on structural response. A quasi-steady load model is adopted, which is able to deal with the considered problems by using experimental data easily available in the practice. By means of numerical examples, it is pointed out (1) that both the modifications in structural tangential stiffness and in the aerodynamic coefficients due to the mean steady deformation may affect the aeroelastic stability threshold and (2) that load linearization may produce an underestimation of the structural response.     

A single degree of freedom ‘lollipop’ model for carbon nanotube bundle formation

Current carbon nanotube (CNT) synthesis methods include the production of ordered, free-standing vertically aligned arrays, the properties of which are partially governed by interactions between adjacent tubes. Using material parameters determined by atomistic methods, here we represent individual CNTs by a simple single degree of freedom ‘lollipop’ model to investigate the formation, mechanics, and self-organization of CNT bundles driven by weak van der Waals interactions. The computationally efficient simple single degree of freedom model enables us to study arrays consisting of hundreds of thousands of nanotubes. The effects of nanotube parameters such as aspect ratio, bending stiffness, and surface energy, on formation and bundle size, as well as the intentional manipulation of bundle pattern formation, are investigated. We report studies with both single wall carbon nanotubes (SWCNTs) and double wall carbon nanotubes (DWCNTs) with varying aspect ratios (that is, varying height). We calculate the local density distributions of the nanotube bundles and show that there exists a maximum attainable bundle density regardless of an increase in surface energy for nanotubes with given spacing and stiffness. In addition to applications to CNTs, our model can also be applied to other types of nanotube arrays (e.g. protein nanotubes, polymer nanofilaments).     

A variational ensemble Kalman filtering method for data assimilation using 2D and 3D version of COHERENS model

Decoupled implementation of data assimilation methods has been rarely studied. The variational ensemble Kalman filter has been implemented such that it needs not to communicate directly with the model, but only through input and output devices. In this work, an open multi‐functional three‐dimensional (3D) model, the coupled hydrodynamical‐ecological model for regional and shelf seas (COHERENS), has been used. Assimilation of the total suspended matter (TSM) is carried out in 154 km² lake Säkylän Pyhäjärvi. Observations of TSM were derived from high‐resolution satellite images of turbidity and chrolophyll‐a. For demonstrating the method, we have used a low‐resolution model grid of 1 km. The model was run for a period from May 16 to September 14. We have run the COHERENS model with two‐dimensional (2D) mode time steps and 3D mode time steps. This allows COHERENS to switch between 2D and 3D modes in a single run for computational efficiency. We have noticed that there is not much difference between these runs. This is because satellite images depict the derived TSM for the surface layer only. The use of additional 3D data might change this conclusion and improve the results. We have found that in this study, the use of a large ensemble size does not guarantee higher performance. The successful implementation of decoupled variational ensemble Kalman filter method opens the way for other methods and evolution models to enjoy the benefits without having to spend substantial effort in merging the model and assimilation codes together, which can be a difficult task. © 2016 The Authors. International Journal for Numerical Methods in Fluids Published by John Wiley & Sons Ltd.     

Dynamic analysis of the double crank mechanism with a 3D translational clearance joint employing a variable stiffness contact force model

Nonlinear Dynamics - Oblique collisions are more likely to happen in the realistic translational joint with clearance, compared to the full front impacts. It can be a quite demanding task to...     

A comprehensive model for 3D revolute joints with clearances in mechanical systems

Nonlinear Dynamics - A mechanical system with clearance joints is well known as a nonlinear dynamic system that may exhibit chaotic responses under certain conditions. In the previous literature,...     

A 3D model of the cyclic thermomechanical behavior of shape memory alloys

The model in the first part of this paper is extended to account for SMA behavior under cyclic loading. To this end, three new state variables are introduced: internal stress B, residual strain ?_r and cumulated martensite volume fraction z_e. Several parameters of the extended model depend on z_e, making them evolve with cyclic phase change. Cyclic SMA effects including training and two-way shape memory are accounted for and several numerical simulations are provided and validated in the case of cyclic superelasticity.     

A γ‐model BGK scheme for compressible multifluids

We present a γ‐model BGK scheme for the numerical simulation of compressible multifluids. The scheme is based on the incorporation of a conservative γ‐model scheme given in (J. Comput. Phys. 1996; 125 :150–160) into the gas kinetic BGK scheme (J. Comput. Phys. 1993; 109 :53–66, J. Comput. Phys. 1994; 114 :9–17), and is simple to implement. Several numerical examples presented in this paper validate the scheme in the application of compressible multimaterial flows. Copyright © 2004 John Wiley & Sons, Ltd.     

A study of heat transfer for single and double layer inclined synchrotron radiation absorbers

The heat transfer phenomena for single and double layer inclined absorbers which absorb synchrotron radiation has been studied using analytical and numerical methods. Photon penetration through the metal layers has been included and the effects of the spectral variation of the absorption coefficients and variable thermal conductivities have been examined. Different thickness ratios and inclination angles have been studied for double layer absorbers and it has been shown that double layer inclined absorbers significantly reduce the peak temperatures.Das Wärmeübertragungsphenomen bei Synchrotron-Strahlung absorbierenden Ein- und Zweischicht-Schrägabsorbern wurde mit Hilfe von analytischen und numerischen Verfahren untersucht. Die Durchdringung der Metallschichten von Photonen ist auch Teil der Studie gewesen, und die Wirkungen der Spektralvariation der Absorptionskoeffizienten und variablen Wärmeleitfähigkeiten wurden erforscht. Es wurden unterschiedliche Dickenverhältnisse und Neigungswinkel für Zweischicht-Absorber untersucht, und es wird gezeigt, daß Zweischicht-Schrägabsorber die Spitzentemperaturen wesentlich reduzieren.     

A pseudo 3D cooling heat sink model designed by multi-objective topology optimization method

Meccanica - This paper designs a water-cooled pseudo 3D heat sink structure using two-layer heat sink model applying the topology optimization method (TOM) based on rational approximation of...     

Non‐hydrostatic 3D free surface layer‐structured finite volume model for short wave propagation

In this paper a layer‐structured finite volume model for non‐hydrostatic 3D environmental free surface flow is presented and applied to several test cases, which involve the computation of gravity waves. The 3D unsteady momentum and mass conservation equations are solved in a collocated grid made of polyhedrons, which are built from a 2D horizontal unstructured mesh, by just adding several horizontal layers. The mesh built in such a way is unstructured in the horizontal plane, but structured in the vertical direction. This procedure simplifies the mesh generation and at the same time it produces a well‐oriented mesh for stratified flows, which are common in environmental problems. The model reduces to a 2D depth‐averaged shallow water model when one single layer is defined in the mesh. Pressure–velocity coupling is achieved by the Semi‐Implicit Method for Pressure‐Linked Equations algorithm, using Rhie–Chow interpolation to stabilize the pressure field. An attractive property of the model proposed is the ability to compute the propagation of short waves with a rather coarse vertical discretization. Several test cases are solved in order to show the capabilities and numerical stability of the model, including a rectangular free oscillating basin, a radially symmetric wave, short wave propagation over a 1D bar, solitary wave runup on a vertical wall, and short wave refraction over a 2D shoal. In all the cases the numerical results are compared either with analytical or with experimental data. Copyright © 2008 John Wiley & Sons, Ltd.     

A 3D finite strain phenomenological constitutive model for shape memory alloys considering martensite reorientation

Most devices based on shape memory alloys experience both finite deformations and non-proportional loading conditions in engineering applications. This motivates the development of constitutive models considering finite strain as well as martensite variant reorientation. To this end, in the present article, based on the principles of continuum thermodynamics with internal variables, a three-dimensional finite strain phenomenological constitutive model is proposed taking its basis from the recent model in the small strain regime proposed by Panico and Brinson (J Mech Phys Solids 55:2491–2511, 2007). In the finite strain constitutive model derivation, a multiplicative decomposition of the deformation gradient into elastic and inelastic parts, together with an additive decomposition of the inelastic strain rate tensor into transformation and reorientation parts is adopted. Moreover, it is shown that, when linearized, the proposed model reduces exactly to the original small strain model.     

A semi-implicit lagrangian scheme for 3D shallow water flow with a two-layer turbulence model

A semi-implicit Lagrangian finite difference scheme for 3D shallow water flow has been developed to include an eddy viscosity model for turbulent mixing in the vertical direction. The α-co-ordinate system for the vertical direction has been introduced to give accurate definition of bed and surface boundary conditions. The simple two-layer mixing length model for rough surfaces is used with the standard assumption that the shear stress across the wall region at a given horizontal location is constant. The bed condition is thus defined only by its roughness height (avoiding the need for a friction formula relating to depth-averaged flow, e.g. Chezy, used previously). The method is shown to be efficient and stable with an explicit Lagrangian formulation for convective terms and terms for surface elevation and vertical mixing handled implicitly. The method is applied to current flow around a circular island with gently sloping sides which produce periodic recirculation zones (vortex shedding). Comparisons are made with experimental measurements of velocity using laser Doppler anemometry (time histories at specific points) and surface particle-tracking velocimetry.     

Implicit meanflow–multigrid algorithms for Reynolds stress model computation of 3‐D anisotropy‐driven and compressible flows

The present paper investigates the multigrid (MG) acceleration of compressible Reynolds‐averaged Navier–Stokes computations using Reynolds‐stress model 7‐equation turbulence closures, as well as lower‐level 2‐equation models. The basic single‐grid SG algorithm combines upwind‐biased discretization with a subiterative local‐dual‐time‐stepping time‐integration procedure. MG acceleration, using characteristic MG restriction and prolongation operators, is applied on meanflow variables only (MF–MG), turbulence variables being simply injected onto coarser grids. A previously developed non‐time‐consistent (for steady flows) full‐approximation‐multigrid (s–MG) is assessed for 3‐D anisotropy‐driven and/or separated flows, which are dominated by the convergence of turbulence variables. Even for these difficult test cases CPU‐speed‐ups r_CPUSUP∈[3, 5] are obtained. Alternative, potentially time‐consistent approaches (unsteady u–MG), where MG acceleration is applied at each subiteration, are also examined, using different subiterative strategies, MG cycles, and turbulence models. For 2‐D shock wave/turbulent boundary layer interaction, the fastest s–MG approach, with a V(2, 0) sawtooth cycle, systematically yields CPU‐speed‐ups of 5±½, quasi‐independent of the particular turbulence closure used. Copyright © 2008 John Wiley & Sons, Ltd.