Kinematic Boundary Conditions Research Articles

Development of a Tsunami Inundation Analysis Model for Urban Areas Using a Porous Body Model

To evaluate tsunami hazards with strong locality in urban areas, this study developed a novel tsunami inundation model based on nonlinear shallow water wave equations and a porous body model (PBM). By applying a kinematic boundary condition that includes both porosity and surface permeability of the porous medium, the proposed model could accurately incorporate geometric effects such as the flow anisotropy caused by the distributions of buildings. The proposed PBM demonstrated as good accuracy for the inundation heights around buildings near the coastline as with a conventional three-dimensional simulation with high resolution. In addition, the model showed its capability to reproduce a tsunami’s essential behaviors in urban areas. In particular, the amplification effect of flow velocity along straight roads surrounded by buildings was reasonably reproduced. It can be expected that the present model can become a useful tool to accurately evaluate the tsunami risks in urban areas.

On a Model for a Sliding Droplet: Well-posedness and Stability of Translating Circular Solutions

In this paper the model for a highly viscous droplet sliding down an inclined plane is analyzed. It is shown that, provided the slope is not too steep, the corresponding moving boundary problem possesses classical solutions. Well-posedness is lost when the relevant linearization ceases to be parabolic. This occurs above a critical incline which depends on the shape of the initial wetted region as well as on the liquid's mass. It is also shown that translating circular solutions are asymptotically stable if the kinematic boundary condition is given by an affine function and provided the incline is small.

Tsunami hazard evaluation for Kuwait and Arabian Gulf due to Makran Subduction Zone and Subaerial landslides

Given the recent historical disastrous tsunamis and the knowledge that the Arabian Gulf (AG) is tectonically active, this study aimed to evaluate tsunami hazards in Kuwait from both submarine earthquakes and subaerial landslides. Despite the low or unknown tsunami risks that impose potential threats to the coastal area’s infrastructures and population of Kuwait, such an investigation is important to sustain the economy and safety of life. This study focused on tsunamis generated by submarine earthquakes with earthquake magnitudes (M w ) of 8.3–9.0 along the Makran Subduction Zone (MSZ) and subaerial landslides with volumes of 0.75–2.0 km3 from six sources along the Iranian coast inside the AG and one source at the Gulf entrance in Oman. The level of tsunami hazards associated with these tsunamigenic sources was evaluated using numerical modeling. Tsunami model was applied to conduct a numerical tsunami simulation and predict tsunami propagation. For landslide sources, a two-layer model was proposed to solve nonlinear longwave equations within two interfacing layers with appropriate kinematic and dynamic boundary conditions. Threat level maps along the coasts of the AG and Kuwait were developed to illustrate the impacts of potential tsunamis triggered by submarine earthquakes of different scales and subaerial landslides at different sources. GEBCO 30 arc-second grid data and others were used as bathymetry and topography data for numerical modeling. Earthquakes of M w 8.3 and M w 8.6 along the MSZ had low and considerable impacts, respectively, at the Gulf entrance, but negligible impacts on Kuwait. An earthquake of M w 9.0 had a remarkable impact for the entire Gulf region and generated a maximum tsunami amplitude of up to 0.5 m along the Kuwaiti coastline 12 h after the earthquake. In the case of landslides inside the AG, the majority impact occurred locally near the sources. The landslide source opposite to Kuwait Bay generated the maximum tsunami amplitudes reaching 0.3 m inside Kuwait Bay and 1.8 m along the southern coasts of Kuwait.

A Rayleigh-Ritz approach for postbuckling analysis of variable angle tow composite stiffened panels

A Rayleigh-Ritz solution approach for generally restrained multilayered variable angle tow stiffened plates in postbuckling regime is presented. The plate model is based on the first order shear deformation theory and accounts for geometrical nonlinearity through the von Kármán’s assumptions. Stiffened plates are modelled as assembly of plate-like elements and penalty techniques are used to join the elements in the assembled structure and to apply the kinematical boundary conditions. General symmetric and unsymmetric stacking sequences are considered and Legendre orthogonal polynomials are employed to build the trial functions. A computer code was developed to implement the proposed approach and to establish its applicability and its features for investigating variable angle tow structures. The proposed solution is validated by comparison with literature and finite elements results. Original results are presented for postbuckling of variable angle tow stiffened plates showing the potentialities of the method.

Experimental Investigation on the Effects of the Fixed Boundaries in Channelized Dry Granular Flows

The dynamics of granular mixtures, involved in several geophysical phenomena like rock avalanches and debris flows, is far from being completely understood. Several features of their motion, such as non-local and boundary effects, still represent open problems. An extensive experimental study on free-surface channelized granular flows is here presented, where the effects of the fixed boundaries are systematically investigated. The entire experimental data set is obtained by using a homogenous acetal-polymeric granular material and three different basal surfaces, allowing different kinematic boundary conditions. Velocity profiles at both the sidewall and the free surface are obtained by using high-speed cameras and the open-source particle image velocimetry code, PIVlab. Significantly, different sidewall velocity profiles are observed by varying the basal roughness and the flow depth. Owing to sidewall friction and non-local effects, such profiles exhibit a clear rheological stratification for high enough flow depths and they can be well described by recurring to composite functions, variously formed of linear, Bagnold and exponential scalings. Moreover, it has been discovered that transitions from one velocity profile to another are also possible on the same basal surface by merely varying the flow depth. This shape transition is due partly to the sidewall resistances, the basal boundary condition and, in particular, the occurrence/inhibition of basal grain rolling. In most of the experiments, the normal-to-bed velocity profiles and the velocity measurements at the free surface strongly suggest the occurrence of a secondary circulating flow, made possible by a chiefly collisional regime beneath the free surface.

Minimal Kinematic Boundary Conditions for Computational Homogenization of the Permeability Coefficient

Abstract In the paper, computational homogenization approach is used for recognizing the macroscopic permeability from the microscopic representative volume element (RVE). Flow of water, at both macro and micro level, is assumed to be ruled by Darcy law. A special averaging constraint is used for numerical flow analysis in RVE, which allows to apply macroscopic pressure gradient without the necessity to use directly Dirichlet or Neumann boundary conditions. This approach allows arbitrarily shaped representative volumes and eliminates undesirable boundary effects. Generated effective permeability takes into account the structuring effects, what is an advantage over other homogenization methods, like self-consistent one.

An arbitrary Lagrangian‐Eulerian framework with exact mass conservation for the numerical simulation of 2D rising bubble problem

SummaryAn arbitrary Lagrangian‐Eulerian framework, which combines the advantages of both Lagrangian and Eulerian methods, is presented to solve incompressible multiphase flow problems. The incompressible Navier‐Stokes equations are discretized using the side‐centered unstructured finite volume method, where the velocity vector components are defined at the midpoint of each cell face, while the pressure term is defined at element centroids. The pressure field is treated to be discontinuous across the interface with the discontinuous treatment of density and viscosity. The surface tension term at the interface is treated as a force tangent to the interface and computed with several different approaches including the use of Legendre polynomials. In addition, the several different discretizations of interface kinematic boundary conditions are investigated. For the application of the interface kinematic boundary condition, a special attention is given to satisfy both local and global discrete geometric conservation law to conserve the total mass of both species at machine precision. The mesh vertices are deformed by solving the linear elasticity equations due to the normal displacement of interface. The resulting algebraic equations are solved in a fully coupled manner, and a one‐level restricted additive Schwarz preconditioner with a block‐incomplete factorization within each partitioned subdomain is used for the resulting fully coupled system. The method is validated by simulating the classical benchmark problem of a single rising bubble in a viscous fluid due to buoyancy. The results of numerical simulations are found out to be in an excellent agreement with the earlier results in the literature. The mass of the bubble is conserved, and discontinuous pressure field is obtained to avoid errors due to the incompressibility condition in the vicinity of the interface, where the density and viscosity jumps occur.

Thermo-mechanical post-buckling analysis of variable angle tow composite plate assemblies

The increasing use of composite materials for lightweight structural applications and the extended tailoring capabilities offered by variable stiffness laminates requires rapid and robust analysis tools that adequately describe the mechanical behaviour of such structures. In this work, a Rayleigh–Ritz solution for generally restrained multilayered stiffened variable angle tow plates in the post-buckling regime is presented. The plate model is based on first-order shear deformation theory and accounts for geometrical nonlinearity through von Kármán’s assumptions. General symmetric and unsymmetric stacking sequences are considered and Legendre orthogonal polynomials are employed to approximate the unknown displacement field. Stiffened variable angle tow plates are modeled as an assembly of plate-like elements and penalty techniques are used to enforce the displacements continuity of the assembled multidomain structure and also to apply the kinematical boundary conditions. The developed postbuckling analysis is sufficiently versatile to model a wide range of configurations and load cases for multi-component, variable angle tow, composite structures, and provide the same accuracy level as finite element analysis. The proposed solution is validated by comparison with literature and finite elements analysis and original results are presented for the thermo-mechanical post-buckling solution of multilayered stiffened variable angle tow plates. The effectiveness of the developed analysis tool for both stiffened plates and a tapered stiffened wing box is shown, with a reduced number of unknowns and simplified data preparation compared to finite element analysis.

Development and validation of a Lagrangian method for 3D turbulent flows with curvilinear free-surface

A numerical model was developed based on a moving grid method for simulating three-dimensional turbulent flows affected by curvilinear free surface. Reynolds-Averaged Navier–Stokes equations with the k–e turbulence model were solved in non-orthogonal curvilinear coordinates. In the free surface, the kinematic boundary condition was implicitly imposed in the pressure Poisson equation derived from the momentum and continuity equations. The water surface elevation was calculated at each time step without solving additional equations. The developed numerical model was validated using the experimental data of the strongly curved channels and submerged hydraulic jump. The numerical simulation of the flow field and free surface elevation in all cases were compared with the experimental results. The agreement between the simulated and measured results was satisfactory for three-dimensional turbulent flows in the strongly curved channels and submerged hydraulic jump. The secondary flow and dip phenomena were correctly simulated in strongly curved channels. This numerical model could accurately predict steep water surface gradients in a submerged hydraulic jump. The reasonable results of the numerical simulation demonstrate the capability of the presented Lagrangian method in hydraulic engineering applications. This model provides a suitable method for simulating the free surface in engineering and environmental problems.

An alternative theoretical approach for the derivation of analytic and numerical solutions to thermal Marangoni flows

The primary objective of this short work is the identification of alternate routes for the determination of exact and numerical solutions of the Navier-Stokes equations in the specific case of surface-tension driven thermal convection. We aim to elaborate a theoretical approach in which the typical kinematic boundary conditions required at the free surface by this kind of flows can be replaced by a homogeneous Neumann condition using a class of ‘continuous’ distribution functions by which no discontinuities or abrupt variations are introduced in the model. The rationale for such a line of inquiry can be found (1) in the potential to overcome the typical bottlenecks created by the need to account for a shear stress balance at the free surface in the context of analytic models for viscoelastic and other non-Newtonian fluids and/or (2) in the express intention to support existing numerical (commercial or open-source) tools where the possibility to impose non-homogeneous Neumann boundary conditions is not an option. Both analytic solutions and (two-dimensional and three-dimensional) numerical “experiments” (concerned with the application of the proposed strategy to thermocapillary and Marangoni-Bénard flows) are presented. The implications of the proposed approach in terms of the well-known existence and uniqueness problem for the Navier-Stokes equations are also discussed to a certain extent, indicating possible directions of future research and extension.

A parallel monolithic approach for fluid-structure interaction in a cerebral aneurysm

Abstract A parallel fully-coupled numerical algorithm has been developed for the fluid-structure interaction problem in a cerebral artery with aneurysm. For the fluid part of the problem, an Arbitrary Lagrangian-Eulerian formulation based on the side-centered unstructured finite volume method is employed for the governing incompressible Navier–Stokes equations. The deformation of the solid domain is governed by the constitutive laws for the nonlinear Saint Venant-Kirchhoff material and the classical Galerkin finite element method is used to discretise the governing equations in a Lagrangian frame. The time integration method for the structure domain is based on the Newmark type generalized − α method while the second-order backward difference (BDF2) is used in the fluid domain. A special attention is given to construct an algorithm obeying the local/global discrete geometric conservation laws (DGCL) in order to conserve fluid volume at machine precision when the fluid domain is entirely enclosed by solid domain boundary. Therefore, a compatible kinematic boundary condition is applied at the interface between the solid and fluid domains. The parallel implementation of the present fully coupled unstructured fluid-structure solver is based on the PETSc library and a one-level restricted additive Schwarz preconditioner with a block-incomplete factorization within each partitioned sub-domains is utilized for the resulting fully coupled system. The proposed algorithm is initially validated for a pressure pulse propagating in a flexible tube and the mass conservation accuracy is tested for a thin elastic sphere filled with an incompressible fluid in a circular tube. Then the numerical method is applied to a complicated problem involving unsteady pulsatile blood flow in a cerebral artery with aneurysm as a realistic fluid-structure interaction problem encountered in biomechanics. Various hemodynamic quantities of interest like fluid velocities, blood pressure and wall shear stresses (WSS) are computed as well as the time dependent artery wall deformations.

Modeling of Cementitious Representative Volume Element with Additives

CEMHYD3D has been employed to simulate the representative volume element (RVE) of cementitious systems (Type I cement) containing fly ash (Class F) through a voxel-based finite element analysis (FEA) approach. Three-dimensional microstructures composed of voxels are generated for a heterogeneous cementitious material consisting of various constituent phases. The primary focus is to simulate a cementitious RVE containing fly ash and to present the homogenized macromechanical properties obtained from its analysis. Simple kinematic uniform boundary conditions as well as periodic boundary conditions were imposed on the RVE to obtain the principal and shear moduli. Our current work considers the effect of fly ash percentage on the elastic properties based on the mass and volume replacements. RVEs with lengths of 50, 100 and 200[Formula: see text][Formula: see text] at different degrees of hydration are generated, and the elastic properties are modeled and simulated. In general, the elastic properties of a cementitious RVE with fly ash replacement for cement based on mass and volume differ from each other. Moreover, the finite element (FE) mesh density effect is studied. Results indicate that mechanical properties decrease with increasing mesh density.

Finite Element Stent Modeling for the Postoperative Analysis of Transcatheter Aortic Valve Implantation

In order to evaluate the performance of stents used in transcatheter aortic valve implantation (TAVI), finite element simulations are setup to reconstruct patient-specific contact forces between implant and its surrounding tissue. Previous work used structural beam elements to setup a numerical model of the CoreValve stent used in TAVI and developed a procedure for implementing kinematic boundary conditions from noisy computer tomography (CT) scanning data. This study evaluates element size selection and quantitatively investigates the choice of a linear elastic constitutive model for the Nitinol stent under physiological loading conditions. It is shown that this simplification leads to reliable results and enables a huge reduction in computation time. Further, the procedure used to compensate for noisy postoperative CT data is tested by adding artificial noise. It is concluded that for physiologically relevant loading ranges, the procedure yields convergent results and successfully eliminates the influence of the noise.

آنالیز عددی پروانه نیمه مغروق در حالت آب آزاد با استفاده از توسعه روش المان مرزی بر پایه جریان پتانسیل

Since the design algorithm of partially submerged propeller (PSP) is under the influence of the various geometrical and physical parameters; so a new convenient method and numerical tools is required to flow analysis on propeller and consider the effect of all parameters simultaneously. The aim of this study is the development of boundary element method (BEM) based on potential for PSP analysis under open water condition. Using the concept of material derivative and kinematic boundary condition, a BEM algorithm has been developed to analyze the growth, development and change in thickness of ventilation-cavitation regimes in both chord and radial directions on wide range of advance velocity coefficients. Based on the obtained results, in the high advance coefficients there are very good conformity between the values obtained from the numerical simulation compared with experimental data and observations. This adaptation is reduced by reducing the value of advance coefficient. For the low advance coefficients ((J 0.4), hydrodynamic coefficients obtained from numerical results and efficiency of propeller compared with experimental measurements are desirable.

A (non-)hydrostatic free-surface numerical model for two-layer flows

A semi-implicit (non-)hydrostatic free-surface numerical model for two layer flows is derived from the Navier–Stokes equations by applying kinematic boundary conditions at moving interfaces and by decomposing the pressure into the hydrostatic and the hydrodynamic part. When the latter is ignored, the algorithm conveniently transforms into a solver for a hydrostatic flow. In addition, when the vertical grid spacing is larger than the layer depths, the algorithm naturally degenerates into a solver for the shallow water equations. In this paper, the presented numerical model is developed for the horizontal centrifugal casting, a metallurgical process, in which a liquid metal is poured into a horizontally rotating cylindrical mold. The centrifugal force pushes the liquid metal toward the mold wall resulting in a formation of a sleeve with a uniform thickness. The mold gradually extracts the sensible and the latent heat from the sleeve, which eventually becomes solid. Often a second layer of another material is introduced during the solidification of the first layer. The proposed free-surface model is therefore coupled with the heat advection-diffusion equation with a stiff latent heat source term representing the solidification. The numerical results show a good agreement with measurements of temperatures performed in the plant. A validation of the proposed model is also provided with the help of using other numerical techniques such as the approximate Riemann solver for the two layer shallow water equations and the volume of fluid method.

Iterative Rankine HOBEM analysis of hull-form effects in forward-speed diffraction problem

A time-domain numerical algorithm based on the higher-order boundary element method and the iterative time-marching scheme is proposed for seakeeping analysis. The ship waves generated by a hull advancing at a constant forward speed in incident waves and the resultant diffraction forces acting on the hull are computed to investigate the hull-form effects on the hydrodynamic forces. A rectangular computational domain travelling at ship's speed is considered. An artificial damping beach for satisfying the radiation condition is installed at the outer portion of the free surface except the downstream side. An iterative time-marching scheme is employed for updating both kinematic and dynamic free-surface boundary conditions for numerical accuracy and stability. The boundary integral equation is solved by distributing higher-order boundary elements over the wetted body surface and the free surface. The hull-form effects on the naval hydrodynamics are investigated by comparing three different Wigley models. Finally, the corresponding unsteady wave patterns and the wave profiles around the hulls are illustrated and discussed.

Application of gradient elasticity to armchair carbon nanotubes: Size effects and constitutive parameters assessment

The central focus of the paper is set on modelling of bending of armchair carbon nanotubes by means of the gradient elasticity theory. Influence of small-size effects on the Young's modulus is investigated. An attempt to determine small size (or nonlocal) parameter employed in the Bernoulli-Euler and Timoshenko gradient formulations is presented. To obtain such a goal, the paper provides an extensive set of molecular structural mechanics simulations of armchair nanotubes with different loading and kinematic boundary conditions. Dependence of the Young's modulus on small size effects is clearly noticed. Based on these results, small scale parameters for the gradient model are identified and limits of the method are pointed out. Results of the study indicate that the widely used theory should be modified to obtain a physically justified and reliable nanobeam model based on Bernoulli-Euler or Timoshenko kinematic assumptions.

Convective wave breaking in the KdV equation

The KdV equation is a model equation for waves at the surface of an inviscid incompressible fluid, and it is well known that the equation describes the evolution of unidirectional waves of small amplitude and long wavelength fairly accurately if the waves fall into the Boussinesq regime. The KdV equation allows a balance of nonlinear steepening effects and dispersive spreading which leads to the formation of steady wave profiles in the form of solitary waves and cnoidal waves. While these wave profiles are solutions of the KdV equation for any amplitude, it is shown here that there for both the solitary and the cnoidal waves, there are critical amplitudes for which the horizontal component of the particle velocity matches the phase velocity of the wave. Solitary or cnoidal solutions of the KdV equation which surpass these amplitudes feature incipient wave breaking as the particle velocity exceeds the phase velocity near the crest of the wave, and the model breaks down due to violation of the kinematic surface boundary condition. The condition for breaking can be conveniently formulated as a convective breaking criterion based on the local Froude number at the wave crest. This breaking criterion can also be applied to time-dependent situations, and one case of interest is the development of an undular bore created by an influx at a lateral boundary. It is shown that this boundary forcing leads to wave breaking in the leading wave behind the bore if a certain threshold is surpassed.

Instability of Viscoelastic Plates with Longitudinally Variable Speed and Immersed in Ideal Liquid

The instability of longitudinally variable speed viscoelastic plates in contact with ideal liquid is studied for the first time. The effect of free surface waves is taken into account in the present study. The viscoelasticity is considered by using the Kelvin–Voigt viscoelastic constitutive relations. The classical theory of thin plate is utilized to derive the governing equation of variable speed plates. The fluid is assumed to be incompressible, inviscid and irrotational. Additionally, the velocity potential and Bernoulli’s equation are utilized to describe the fluid pressure acting on the vibrating plates. The fluid effect on the vibrational plates is described as the added mass of the plates which can be formulated by the kinematic boundary conditions at the structure–fluid interfaces. Parametric instability is analyzed by directly applying the method of multiple scales to the governing partial-differential equations and boundary conditions. The unstable boundaries are derived from the solvability conditions and the Routh–Hurwitz criterion for principal parametric, sum-type and difference-type combination resonances. Based on the numerical simulation, the effects of some key parameters on the unstable boundaries are illustrated in the excitation frequency and excitation amplitude plane in detail.

Qualitative description of the particle trajectories for the <i>N</i>-solitons solution of the Korteweg-de Vries equation

The qualitative properties of the particle trajectories of the $N$-solitons solution of the KdV equation are recovered from the first order velocity field by the introduction of the stream function. Numerical simulations show an accurate depth dependance of the particles trajectories for solitary waves. Failure of the free surface kinematic boundary condition for the first order type velocity field is highlighted.