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Free Surface (free + surface)
Terms modified by Free Surface Selected AbstractsThree-dimensional study of the pressure field and advantages of hemispherical crucible in silicon Czochralski crystal growthCRYSTAL RESEARCH AND TECHNOLOGY, Issue 6 2010F. Mokhtari Abstract The effects of several growth parameters in cylindrical and spherical Czochralski crystal process are studied numerically and particularly, we focus on the influence of the pressure field. We present a set of three-dimensional computational simulations using the finite volume package Fluent in two different geometries, a new geometry as cylindro-spherical and the traditional configuration as cylindro-cylindrical. We found that the evolution of pressure which is has not been studied before; this important function is strongly related to the vorticity in the bulk flow, the free surface and the growth interface. It seems that the pressure is more sensitive to the breaking of symmetry than the other properties that characterize the crystal growth as temperature or velocity fields. (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Numerical study of influences of buoyancy and solutal Marangoni convection on flow structures in a germanium-silicon floating zoneCRYSTAL RESEARCH AND TECHNOLOGY, Issue 6 2005K. Lin Abstract This paper presents a numerical study of Marangoni flows in a floating zone of germanium-silicon crystals, which was performed by using a commercial finite element program FIDADTM. The numerical results point out that for fluids with a small Pr number the influence of buoyancy forces cannot be ignored in the numerical model. Furthermore, the competition between the thermocapillary (TC) and solutocapillary (SC) flows in the floating zones was qualitatively examined. If the TC flow is as strong as that in the Si-rich floating zone, the SC flow may be restricted to the bottom area near the free surface. Otherwise, the SC flow may overcome the TC flow and induce a surface transfer of species. The numerical predictions agree well with the previous experiment results. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Response of unbounded soil in scaled boundary finite-element methodEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 1 2002John P. Wolf Abstract The scaled boundary finite-element method is a powerful semi-analytical computational procedure to calculate the dynamic stiffness of the unbounded soil at the structure,soil interface. This permits the analysis of dynamic soil,structure interaction using the substructure method. The response in the neighbouring soil can also be determined analytically. The method is extended to calculate numerically the response throughout the unbounded soil including the far field. The three-dimensional vector-wave equation of elasto-dynamics is addressed. The radiation condition at infinity is satisfied exactly. By solving an eigenvalue problem, the high-frequency limit of the dynamic stiffness is constructed to be positive definite. However, a direct determination using impedances is also possible. Solving two first-order ordinary differential equations numerically permits the radiation condition and the boundary condition of the structure,soil interface to be satisfied sequentially, leading to the displacements in the unbounded soil. A generalization to viscoelastic material using the correspondence principle is straightforward. Alternatively, the displacements can also be calculated analytically in the far field. Good agreement of displacements along the free surface and below a prism foundation embedded in a half-space with the results of the boundary-element method is observed. Copyright © 2001 John Wiley & Sons, Ltd. [source] Finite element analysis of corner point displacements and stress intensity factors for narrow notches in square sheets and platesFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 12 2000L. P. Pook It is possible to model a crack as a narrow parallel-sided notch with a semicircular tip. Surface displacements of narrow notches in the vicinity of a corner point where the notch tip intersects a free surface were investigated, using finite element analysis, for each of the three modes of crack tip surface displacement. Some reasonably accurate relevant stress intensity factors were determined by analysis of notch tip stresses. The extent of corner regions in which stress intensity measures, rather than stress intensity factors, dominate crack tip stresses was determined by analysis of the notch surface displacements and of relevant stress intensity factors. Under nominal Mode III loading corner point effects are local, but under nominal Mode I and nominal Mode II loadings they are a combination of local and global effects. Volterra distorsioni are useful in the description of crack, and narrow notch, surface displacements under load. [source] The effects of diel changes in circulation and mixing on the longitudinal distribution of phytoplankton in a canyon-shaped Mediterranean reservoirFRESHWATER BIOLOGY, Issue 9 2010JAVIER VIDAL Summary 1. The near-surface distribution of phytoplankton cells along the thalweg of a canyon-shaped reservoir (El Gergal, southern Spain) during two surveys is described and interpreted as the result of time-varying large-scale circulation patterns, vertical mixing processes and the physiological capacity of algal cells to regulate its position in the water column. 2. Vertical gradients of chlorophyll-a concentration developed in the water column during the day but disappeared at night, as a result of the shoaling and deepening of the diurnal mixed layer (dml). The changes in the depth of the dml are largely controlled in El Gergal by convectively driven mixing processes. The longitudinal circulation changes, in turn, as a result of weak and diurnal land-sea breezes. The distribution of algal cells was patchy at all times but did not change during any of the surveys. 3. An expression is proposed to estimate time scales for the development of horizontal patchiness TP based on simple concepts of transport. It is shown that TP is in the order of a week, indicating that horizontal patchiness does not respond immediately to hourly changes in the controlling factors. The magnitude of TP, though, depends on how the vertical distribution of chlorophyll-a and longitudinal currents change on subdiurnal time scales. In particular, TP is sensitive to the lag existing between the momentum and heat fluxes through the free surface, driving circulation and vertical mixing. [source] Parsimonious finite-volume frequency-domain method for 2-D P,SV -wave modellingGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2008R. Brossier SUMMARY A new numerical technique for solving 2-D elastodynamic equations based on a finite-volume frequency-domain approach is proposed. This method has been developed as a tool to perform 2-D elastic frequency-domain full-waveform inversion. In this context, the system of linear equations that results from the discretization of the elastodynamic equations is solved with a direct solver, allowing efficient multiple-source simulations at the partial expense of the memory requirement. The discretization of the finite-volume approach is through triangles. Only fluxes with the required quantities are shared between the cells, relaxing the meshing conditions, as compared to finite-element methods. The free surface is described along the edges of the triangles, which can have different slopes. By applying a parsimonious strategy, the stress components are eliminated from the discrete equations and only the velocities are left as unknowns in the triangles. Together with the local support of the P0 finite-volume stencil, the parsimonious approach allows the minimizing of core memory requirements for the simulation. Efficient perfectly matched layer absorbing conditions have been designed for damping the waves around the grid. The numerical dispersion of this FV formulation is similar to that of O(,x2) staggered-grid finite-difference (FD) formulations when considering structured triangular meshes. The validation has been performed with analytical solutions of several canonical problems and with numerical solutions computed with a well-established FD time-domain method in heterogeneous media. In the presence of a free surface, the finite-volume method requires 10 triangles per wavelength for a flat topography, and fifteen triangles per wavelength for more complex shapes, well below the criteria required by the staircase approximation of O(,x2) FD methods. Comparisons between the frequency-domain finite-volume and the O(,x2) rotated FD methods also show that the former is faster and less memory demanding for a given accuracy level, an attractive feature for frequency-domain seismic inversion. We have thus developed an efficient method for 2-D P,SV -wave modelling on structured triangular meshes as a tool for frequency-domain full-waveform inversion. Further work is required to improve the accuracy of the method on unstructured meshes. [source] A semi-spectral modelling of landslide tsunamisGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2008Nazmi Postacioglu SUMMARY A new, semi-spectral technique based on integral equations is introduced for the landslide tsunami problem. The technique does not use the shallow water approximation and resolves the dispersive surface wavefield generated by sliding material over a bathymetric profile. The wave scattering due to the bathymetric profile on which the slide occurs is calculated solving an integral equation. On the free surface, the linearized kinematic and dynamic boundary conditions are imposed. Method of images is adopted to solve for a source-sink distribution on the bathymetry to simulate the motion of the landslide and to satisfy the kinematic condition on the sea bottom. An asymptotic relation for the far field is also derived. The application to a landslide tsunami generation scenario in the Sea of Marmara reveals that a thickness H submarine mass failure on the southern rim of the Ç,narc,k Basin would create a wave peak of around 0.5 H on the ,1000 m deep Ç,narc,k Basin. [source] Body-wave traveltime and amplitude shifts from asymptotic travelling wave couplingGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2006F. Pollitz SUMMARY We explore the sensitivity of finite-frequency body-wave traveltimes and amplitudes to perturbations in 3-D seismic velocity structure relative to a spherically symmetric model. Using the approach of coupled travelling wave theory, we consider the effect of a structural perturbation on an isolated portion of the seismogram. By convolving the spectrum of the differential seismogram with the spectrum of a narrow window taper, and using a Taylor's series expansion for wavenumber as a function of frequency on a mode dispersion branch, we derive semi-analytic expressions for the sensitivity kernels. Far-field effects of wave interactions with the free surface or internal discontinuities are implicitly included, as are wave conversions upon scattering. The kernels may be computed rapidly for the purpose of structural inversions. We give examples of traveltime sensitivity kernels for regional wave propagation at 1 Hz. For the direct SV wave in a simple crustal velocity model, they are generally complicated because of interfering waves generated by interactions with the free surface and the Mohorovi,i, discontinuity. A large part of the interference effects may be eliminated by restricting the travelling wave basis set to those waves within a certain range of horizontal phase velocity. [source] On strike-slip faulting in layered mediaGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2002Maurizio Bonafede Summary We study the effects of structural inhomogeneities on the stress and displacement fields induced by strike-slip faults in layered media. An elastic medium is considered, made up of an upper layer bounded by a free surface and welded to a lower half-space characterized by different elastic parameters. Shear cracks with assigned stress drop are employed as mathematical models of strike-slip faults, which are assumed to be vertical and planar. If the crack is entirely embedded within the lower medium (case A), a Cauchy-kernel integral equation is obtained, which is solved by employing an expansion of the dislocation density in Chebyshev polynomials. If the crack is within the lower medium but it terminates at the interface (case B), a generalized Cauchy singularity appears in the integral kernel. This singularity affects the singular behaviour of the dislocation density at the crack tip touching the interface. Finally, the case of a crack crossing the interface is considered (case C). The crack is split into two interacting sections, each placed in a homogeneous medium and both open at the interface. Two coupled generalized Cauchy equations are obtained and solved for the dislocation density distribution of each crack section. An asymptotic study near the intersection between the crack and the interface shows that the dislocation densities for each crack section are bounded at the interface, where a jump discontinuity is present. As a corollary, the stress drop must be discontinuous at the interface, with a jump proportional to the rigidity contrast between the adjoining media. This finding is shown to have important implications for the development of geometrical complexities within transform fault zones: planar strike-slip faults cutting across layer discontinuities with arbitrary stress drop values are shown to be admissible only if the interface between different layers becomes unwelded during the earthquake at the crack/interface junction. Planar strike-slip faulting may take place only in mature transform zones, where a repetitive earthquake cycle has already developed, if the rheology is perfectly elastic. Otherwise, the fault cannot be planar: we infer that strike-slip faulting at depth is plausibly accompanied by en-echelon surface breaks in a shallow sedimentary layer (where the stress drop is lower than prescribed by the discontinuity condition), while ductile deformation (or steady sliding) at depth may be accommodated by multiple fault branching or by antithetic faulting in the upper brittle layer (endowed with lower rigidity but higher stress). [source] A Closed Form Slug Test Theory for High Permeability AquifersGROUND WATER, Issue 1 2005David W. Ostendorf We incorporate a linear estimate of casing friction into the analytical slug test theory of Springer and Gelhar (1991) for high permeability aquifers. The modified theory elucidates the influence of inertia and casing friction on consistent, closed form equations for the free surface, pressure, and velocity fluctuations for overdamped and under-damped conditions. A consistent, but small, correction for kinetic energy is included as well. A characteristic velocity linearizes the turbulent casing shear stress so that an analytical solution for attenuated, phase shifted pressure fluctuations fits a single parameter (damping frequency) to transducer data from any depth in the casing. Underdamped slug tests of 0.3, 0.6, and 1 m amplitudes at five transducer depths in a 5.1 cm diameter PVC well 21 m deep in the Plymouth-Carver Aquifer yield a consistent hydraulic conductivity of 1.5 × 10,3 m/s. The Springer and Gelhar (1991) model underestimates the hydraulic conductivity for these tests by as muchas 25% by improperly ascribing smooth turbulent casing friction to the aquifer. The match point normalization of Butler (1998) agrees with our fitted hydraulic conductivity, however, when friction is included in the damping frequency. Zurbuchen et al. (2002) use a numerical model to establish a similar sensitivity of hydraulic conductivity to nonlinear casing friction. [source] Dynamic response of a soft soil layer to flow and periodical disturbanceINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 11 2003Ping-Cheng Hsieh Abstract The dynamic response of a soft soil layer of finite thickness under the mutual effects of flow and periodical disturbance at the free surface is discussed in this work. The homogeneous water is governed by potential theory and the soil layer obeys Biot's theory of poroelasticity. The boundary-value problem is solved by an analytical algorithm, in which the wave number is found first. Secondly, the closed form solutions are found by a two-parameter perturbation method with the boundary-layer correction. The results are also compared with those of the poroelastic soil layer of infinite thickness to show the impermeable rigid boundary effect. Copyright © 2003 John Wiley & Sons, Ltd. [source] Numerical simulation of the fracture process in cutting heterogeneous brittle materialINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 13 2002H. Y. Liu Abstract The process of cutting homogeneous soft material has been investigated extensively. However, there are not so many studies on cutting heterogeneous brittle material. In this paper, R-T2D (Rock and Tool interaction), based on the rock failure process analysis model, is developed to simulate the fracture process in cutting heterogeneous brittle material. The simulated results reproduce the process involved in the fragmentation of rock or rock-like material under mechanical tools: the build-up of the stress field, the formation of the crushed zone, surface chipping, and the formation of the crater and subsurface cracks. Due to the inclusion of heterogeneity in the model, some new features in cutting brittle material are revealed. Firstly, macroscopic cracks sprout at the two edges of the cutter in a tensile mode. Then with the tensile cracks releasing the confining pressure, the rock in the initially high confining pressure zone is compressed into failure and the crushed zone gradually comes into being. The cracked zone near the crushed zone is always available, which makes the boundary of the crushed zone vague. Some cracks propagate to form chipping cracks and some dip into the rock to form subsurface cracks. The chipping cracks are mainly driven to propagate in a tensile mode or a mixed tensile and shear mode, following curvilinear paths, and finally intersect with the free surface to form chips. According to the simulated results, some qualitative and quantitative analyses are performed. It is found that the back rake angle of the cutter has an important effect on the cutting efficiency. Although the quantitative analysis needs more research work, it is not difficult to see the promise that the numerical method holds. It can be utilized to improve our understanding of tool,rock interaction and rock failure mechanisms under the action of mechanical tools, which, in turn, will be useful in assisting the design of fragmentation equipment and fragmentation operations. Copyright © 2002 John Wiley & Sons, Ltd. [source] Coupled damage and plasticity modelling in transient dynamic analysis of concreteINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 1 2002Fabrice Gatuingt Abstract In a concrete structure subjected to an explosion, for example a concrete slab, the material is subjected to various states of stress which lead to many modes of rupture. Closer to the explosive, a state of strong hydrostatic compression is observed. This state of stress produces an irreversible compaction of the material. Away from the zone of explosion, confinement decreases and the material undergoes compression with a state of stress, which is slightly triaxial. Finally, the compression wave can be reflected on a free surface and becomes a tensile wave, which by interaction with the compression wave, produces scabbing. We present, in this paper, a model aimed at describing these three failure modes. It is based on visco-plasticity and rate dependent damage in which a homogenization method is used in order to include the variation of the material porosity due to compaction. The model predictions are compared with several experiments performed on the same concrete. Computations of split Hopkinson tests on confined concrete, a tensile test with scabbing, and an explosion on a concrete slab are presented. Copyright © 2001 John Wiley & Sons, Ltd. [source] Effect of element size on the static finite element analysis of steep slopesINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 14 2001Scott A. Ashford Abstract The accuracy of the computed stress distribution near the free surface of vertical slopes was evaluated in this study as a function of the element size, including aspect ratio. To accomplish this objective, a parametric study was carried out comparing stresses computed using the finite element method (FEM) to those obtained from a physical model composed of photoelastic material. The results of the study indicate a reasonable agreement between a gelatin model and the FEM model for shear stresses, and an overall good agreement between the two models for the principal stresses. For stresses along the top of the slope, the height of the element tends to be more important than width or aspect ratio, at least for aspect ratios up to 4. In all cases, the greatest difference between the two models occurs in the vicinity of the slope. Specifically, if H is defined as the slope height, an element height of H/10 appears to be adequate for the study of stresses deep within the slope, such as for typical embankment analyses. However, for cases where tensile stresses in the vicinity of the slope face which are critical, such as for the stability analysis of steep slopes, element heights as small as H/32, or higher-order elements, are necessary. Copyright © 2001 John Wiley & Sons, Ltd. [source] The formation of dunes, antidunes, and rapidly damping waves in alluvial channelsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7 2001L.-H. Huang Abstract Under the effect of a constant current for a long time, a water channel of infinitely long and constant depth interacting with a uniform sandbed of infinite thickness is used to simulate the formation of dunes, antidunes and rapidly damping waves in alluvial channels. The theory of potential flow is applied to the channel flow, while Biot's theory of poroelasticity is adopted to deal with erodible bed material. The governing equations, together with free surface, bed surface, and far field boundary conditions, form a complete boundary-value problem without applying empirical sediment discharge formulas as in conventional researches. The comparison of the present result with Kennedy's (Journal of Fluid Mechanics, 1963; 16: 521,544) instability analysis not only indicates the appropriateness of the present work, but also reveals the advantage of the present study due to its ability to find all kinds of bed forms (including the rapidly damping waves that Kennedy could not find) and of solving for the unclear lagged distance , introduced in Kennedy's work. Copyright © 2001 John Wiley & Sons, Ltd. [source] Sloshing analysis of a liquid storage container using level set X-FEMINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 4 2009Toshio Nagashima Abstract The extended finite element method (X-FEM), in conjunction with the level set method, is applied to sloshing analysis of a rigid container filled with liquid. The governing equations for liquid with a free surface based on the potential flow theory are discretized using the framework of level set X-FEM. Once the space domain of a container is modeled by tetrahedral elements, sloshing analysis for arbitrary liquid levels and configurations can be performed without remeshing. Natural frequencies of free surface sloshing motion in rigid containers of various shapes were computed by the proposed method and the results were compared with those obtained by theoretical solutions and experiments. The proposed method was demonstrated to perform sloshing analysis efficiently for rigid containers with various liquid levels and configurations. Copyright © 2008 John Wiley & Sons, Ltd. [source] A combination of implicit and adaptative upwind tools for the numerical solution of incompressible free surface flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 6 2007V. G. Ferreira Abstract This paper is concerned with the numerical solutions of time dependent two-dimensional incompressible flows. By using the primitive variables of velocity and pressure, the Navier,Stokes and mass conservation equations are solved by a semi-implicit finite difference projection method. A new bounded higher order upwind convection scheme is employed to deal with the non-linear (advective) terms. The procedure is an adaptation of the GENSMAC (J. Comput. Phys. 1994; 110:171,186) methodology for calculating confined and free surface fluid flows at both low and high Reynolds numbers. The calculations were performed by using the 2D version of the Freeflow simulation system (J. Comp. Visual. Science 2000; 2:199,210). In order to demonstrate the capabilities of the numerical method, various test cases are presented. These are the fully developed flow in a channel, the flow over a backward facing step, the die-swell problem, the broken dam flow, and an impinging jet onto a flat plate. The numerical results compare favourably with the experimental data and the analytical solutions. Copyright © 2006 John Wiley & Sons, Ltd. [source] Local volume-conserving free surface smoothingINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 2 2007F. S. Sousa Abstract Removing high-frequency undulations in surfaces is a problem that appears in different fields, such as computer graphics and computational fluid mechanics. This problem is typically handled by surface smoothing techniques, such as Laplacian filters, that eliminate high-frequency undulations but degrade the volume encompassed by the surface. The need for conserving volume (or mass) rules out the use of such techniques in several application, as for example incompressible flows. In this work we present a smoothing technique that suppresses undulations while conserving local volumes, ensuring that the global mass is conserved. The effectiveness of the proposed technique is illustrated in synthetic datasets as well as in free surface flows simulation. Comparisons between our smoothing approach and the well-known Laplacian filter are also presented. Copyright © 2006 John Wiley & Sons, Ltd. [source] On the calculation of normals in free-surface flow problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2004M. A. Walkley Abstract The use of boundary-conforming finite element methods is considered for the solution of surface-tension-dominated free-surface flow problems in three dimensions. This class of method is based upon the use of a moving mesh whose velocity is driven by the motion of the free surface, which is in turn determined via a kinematic boundary condition for the normal velocity. The significance of the method used to compute the normal direction at the finite element node points for a C0 piecewise-polynomial free surface is investigated. In particular, it is demonstrated that the concept of mass-consistent normals on an isoparametric quadratic tetrahedral mesh is flawed. In this case an alternative, purely geometric, normal is shown to lead to a far more robust numerical algorithm. Copyright © 2004 John Wiley & Sons, Ltd. [source] Adaptive ICT procedure for non-linear seepage flows with free surface in porous mediaINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3 2002N. H. Sharif Abstract This paper focuses on adaptive finite element (FE)-methods for computation of the motion of viscous fluid interfaces fundamentally encountered in multiphase flow problems in porous media. An interface capturing technique (ICT)-procedure is formulated with a stabilized finite element scheme in a Eulerian framework to solve the two-dimensional (2D) and three-dimensional (3D) Navier,Stokes equation in porous media. Global mesh refinements of the discretized domain and local mesh refinements in the vicinity of the interface are used for the spatial discretization. The ICT is embedded into the finite element scheme by adding an extra advection equation and an additional unbounded degree of freedom to the number of the unknowns. Problems of non-linear free surface seepage flow in earth-fill dams are simulated in order to validate the performance of the FE-ICT. Computations for steady non-linear seepage flows in 2D and 3D are obtained for homogenous, isotropic and isothermal porous media. Copyright © 2002 John Wiley & Sons, Ltd. [source] ODDLS: A new unstructured mesh finite element method for the analysis of free surface flow problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2008Julio Garcia-Espinosa Abstract This paper introduces a new stabilized finite element method based on the finite calculus (Comput. Methods Appl. Mech. Eng. 1998; 151:233,267) and arbitrary Lagrangian,Eulerian techniques (Comput. Methods Appl. Mech. Eng. 1998; 155:235,249) for the solution to free surface problems. The main innovation of this method is the application of an overlapping domain decomposition concept in the statement of the problem. The aim is to increase the accuracy in the capture of the free surface as well as in the resolution of the governing equations in the interface between the two fluids. Free surface capturing is based on the solution to a level set equation. The Navier,Stokes equations are solved using an iterative monolithic predictor,corrector algorithm (Encyclopedia of Computational Mechanics. Wiley: New York, 2004), where the correction step is based on imposing the divergence-free condition in the velocity field by means of the solution to a scalar equation for the pressure. Examples of application of the ODDLS formulation (for overlapping domain decomposition level set) to the analysis of different free surface flow problems are presented. Copyright © 2008 John Wiley & Sons, Ltd. [source] A numerical study of wave structures developed on the free surface of a film flowing on inclined planes and subjected to surface shearINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2006N. H. Shuaib Abstract In this work, we determine the different patterns of possible wave structures that can be observed on a thin film flowing on an inclined plane when at the free surface a shear force (surface traction) is applied. Different wave structures are obtained dependening on the selected combination of downstream and upstream boundary conditions and initial conditions. The resulting initial boundary value problems are solved numerically using the direct BEM numerical solution of the complete two-dimensional Stokes system of equations. In our numerical results, the initial discontinuous shock profiles joining uniform fluid depths are smoothed due to the two-dimensional character of the Stokes formulation, including the effect of the gravitational force as well as the interfacial surface tension force. In this way, physically feasible continuous surface profiles are determined, in which the initial uniform depths are joined by smooth moving wave structures. Numerical solutions have been attained to reproduce the different patterns of possible wave structures previously reported in the literature and extended to identify some other new structures and features defining the behaviour of the surface patterns. Copyright © 2006 John Wiley & Sons, Ltd. [source] A spectral-element method for modelling cavitation in transient fluid,structure interactionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2004M. A. Sprague Abstract In an underwater-shock environment, cavitation (boiling) occurs as a result of reflection of the shock wave from the free surface and/or wetted structure causing the pressure in the water to fall below its vapour pressure. If the explosion is sufficiently distant from the structure, the motion of the fluid surrounding the structure may be assumed small, which allows linearization of the governing fluid equations. In 1984, Felippa and DeRuntz developed the cavitating acoustic finite-element (CAFE) method for modelling this phenomenon. While their approach is robust, it is too expensive for realistic 3D simulations. In the work reported here, the efficiency and flexibility of the CAFE approach has been substantially improved by: (i) separating the total field into equilibrium, incident, and scattered components, (ii) replacing the bilinear CAFE basis functions with high-order Legendre-polynomial basis functions, which produces a cavitating acoustic spectral element (CASE) formulation, (iii) employing a simple, non-conformal coupling method for the structure and fluid finite-element models, and (iv) introducing structure,fluid time-step subcycling. Field separation provides flexibility, as it admits non-acoustic incident fields that propagate without numerical dispersion. The use of CASE affords a significant reduction in the number of fluid degrees of freedom required to reach a given level of accuracy. The combined use of subcycling and non-conformal coupling affords order-of-magnitude savings in computational effort. These benefits are illustrated with 1D and 3D canonical underwatershock problems. Copyright © 2004 John Wiley & Sons, Ltd. [source] Underwater shock-free surface,structure interactionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2003T. G. Liu Abstract A recently developed numerical method has been employed to evaluate the influence of free surface on shock loading in a cylindrical underwater explosion carried out near to both a free surface and a cylindrical rigid structure. In the usual simulation of underwater shock,structure interaction, the shock loading tends to accelerate/move the (rigid) structure only in the resultant force direction. The presence of a free surface and explosion bubble suggests the existence of a reverse loading and provides an additional torque (rotational moment) on the loaded structure. The numerical results also demonstrate the possible existence of a cavitation zone/region in the immediate vicinity of the free surface due to the near-surface underwater explosion. Copyright © 2003 John Wiley & Sons, Ltd. [source] Numerical simulation of free-surface flow using the level-set method with global mass correctionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2010Yali Zhang Abstract A new numerical method that couples the incompressible Navier,Stokes equations with the global mass correction level-set method for simulating fluid problems with free surfaces and interfaces is presented in this paper. The finite volume method is used to discretize Navier,Stokes equations with the two-step projection method on a staggered Cartesian grid. The free-surface flow problem is solved on a fixed grid in which the free surface is captured by the zero level set. Mass conservation is improved significantly by applying a global mass correction scheme, in a novel combination with third-order essentially non-oscillatory schemes and a five stage Runge,Kutta method, to accomplish advection and re-distancing of the level-set function. The coupled solver is applied to simulate interface change and flow field in four benchmark test cases: (1) shear flow; (2) dam break; (3) travelling and reflection of solitary wave and (4) solitary wave over a submerged object. The computational results are in excellent agreement with theoretical predictions, experimental data and previous numerical simulations using a RANS-VOF method. The simulations reveal some interesting free-surface phenomena such as the free-surface vortices, air entrapment and wave deformation over a submerged object. Copyright © 2009 John Wiley & Sons, Ltd. [source] Numerical simulation of bubble and droplet deformation by a level set approach with surface tension in three dimensionsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2010Roberto Croce Abstract In this paper we present a three-dimensional Navier,Stokes solver for incompressible two-phase flow problems with surface tension and apply the proposed scheme to the simulation of bubble and droplet deformation. One of the main concerns of this study is the impact of surface tension and its discretization on the overall convergence behavior and conservation properties. Our approach employs a standard finite difference/finite volume discretization on uniform Cartesian staggered grids and uses Chorin's projection approach. The free surface between the two fluid phases is tracked with a level set (LS) technique. Here, the interface conditions are implicitly incorporated into the momentum equations by the continuum surface force method. Surface tension is evaluated using a smoothed delta function and a third-order interpolation. The problem of mass conservation for the two phases is treated by a reinitialization of the LS function employing a regularized signum function and a global fixed point iteration. All convective terms are discretized by a WENO scheme of fifth order. Altogether, our approach exhibits a second-order convergence away from the free surface. The discretization of surface tension requires a smoothing scheme near the free surface, which leads to a first-order convergence in the smoothing region. We discuss the details of the proposed numerical scheme and present the results of several numerical experiments concerning mass conservation, convergence of curvature, and the application of our solver to the simulation of two rising bubble problems, one with small and one with large jumps in material parameters, and the simulation of a droplet deformation due to a shear flow in three space dimensions. Furthermore, we compare our three-dimensional results with those of quasi-two-dimensional and two-dimensional simulations. This comparison clearly shows the need for full three-dimensional simulations of droplet and bubble deformation to capture the correct physical behavior. Copyright © 2009 John Wiley & Sons, Ltd. [source] Direct numerical simulation of low Reynolds number flows in an open-channel with sidewallsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2010Younghoon Joung Abstract A direct numerical simulation of low Reynolds number turbulent flows in an open-channel with sidewalls is presented. Mean flow and turbulence structures are described and compared with both simulated and measured data available from the literature. The simulation results show that secondary flows are generated near the walls and free surface. In particular, at the upper corner of the channel, a small vortex called inner secondary flows is simulated. The results show that the inner secondary flows, counter-rotating to outer secondary flows away from the sidewall, increase the shear velocity near the free surface. The secondary flows observed in turbulent open-channel flows are related to the production of Reynolds shear stress. A quadrant analysis shows that sweeps and ejections are dominant in the regions where secondary flows rush in toward the wall and eject from the wall, respectively. A conditional quadrant analysis also reveals that the production of Reynolds shear stress and the secondary flow patterns are determined by the directional tendency of the dominant coherent structures. Copyright © 2009 John Wiley & Sons, Ltd. [source] A volume-of-fluid method for incompressible free surface flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2009I. R. Park Abstract This paper proposes a hybrid volume-of-fluid (VOF) level-set method for simulating incompressible two-phase flows. Motion of the free surface is represented by a VOF algorithm that uses high resolution differencing schemes to algebraically preserve both the sharpness of interface and the boundedness of volume fraction. The VOF method is specifically based on a simple order high resolution scheme lower than that of a comparable method, but still leading to a nearly equivalent order of accuracy. Retaining the mass conservation property, the hybrid algorithm couples the proposed VOF method with a level-set distancing algorithm in an implicit manner when the normal and the curvature of the interface need to be accurate for consideration of surface tension. For practical purposes, it is developed to be efficiently and easily extensible to three-dimensional applications with a minor implementation complexity. The accuracy and convergence properties of the method are verified through a wide range of tests: advection of rigid interfaces of different shapes, a three-dimensional air bubble's rising in viscous liquids, a two-dimensional dam-break, and a three-dimensional dam-break over an obstacle mounted on the bottom of a tank. The standard advection tests show that the volume advection algorithm is comparable in accuracy with geometric interface reconstruction algorithms of higher accuracy than other interface capturing-based methods found in the literature. The numerical results for the remainder of tests show a good agreement with other numerical solutions or available experimental data. Copyright © 2009 John Wiley & Sons, Ltd. [source] Non-hydrostatic 3D free surface layer-structured finite volume model for short wave propagationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2009L. Cea Abstract 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. [source] Sigma transformation and ALE formulation for three-dimensional free surface flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2009A. Decoene Abstract In this paper we establish a link between the sigma transformation approach and the arbitrary Lagrangian,Eulerian (ALE) approach. For that purpose we introduce the ALE-sigma (ALES) approach, which consists in an ALE interpretation of the sigma transformation. Taking advantage of this new approach, we propose a general ALES transformation, allowing for a great adaptability of the vertical discretization and therefore overcoming some drawbacks of the classical sigma transformation. Numerical results are presented, showing the advantages of this general coordinate system, as, for example, a better representation of horizontal stratifications. Copyright © 2008 John Wiley & Sons, Ltd. [source] | ||||||||||||||||||||||||||||