Homogenized free surface flow in porous media for wet‐out processing

This paper presents a novel porous media model for homogenized free surface flow, representing wet‐out composites processing. The model is derived from concepts of homogenization applied to a compressible two‐phase flow, accounting for capillary effects and the concept of relative permeability. Based on mass balance considerations, we obtain a nonlinear set of equations of convection‐diffusion type involving the mixture (fluid) pressure and the degree of saturation as primary fields. A staggered Galerkin finite element approach is employed to decouple the solution. Moreover, the streamline upwind/Petrov‐Galerkin technique is applied to attenuate the oscillations in the saturation solutions. The model accuracy and convergence of the finite element solutions are demonstrated through 1‐dimensional and 2‐dimensional examples, representing resin transfer molding flow processes.     

An implicit boundary element solution with consistent linearization for free surface flows and non‐linear fluid–structure interaction of floating bodies

In this work, a new comprehensive method has been developed which enables the solution of large, non‐linear motions of rigid bodies in a fluid with a free surface. The application of the modern Eulerian–Lagrangian approach has been translated into an implicit time‐integration formulation, a development which enables the use of larger time steps (where accuracy requirements allow it). Novel features of this project include: (1) an implicit formulation of the rigid‐body motion in a fluid with a free surface valid for both two or three dimensions and several moving bodies; (2) a complete formulation and solution of the initial conditions; (3) a fully consistent (exact) linearization for free surface flows valid for any boundary elements such that optimal convergence properties are obtained when using a Newton–Raphson solver. The proposed framework has been completed with details on implementation issues referring mainly to the computation of the complete initial conditions and the consistent linearization of the formulation for free surface flows. The second part of the paper demonstrates the mathematical and numerical formulation through numerical results simulating large free surface flows and non‐linear fluid structure interaction. The implicit formulation using a fully consistent linearization based on the boundary element method and the generalized trapezoidal rule has been applied to the solution of free surface flows for the evolution of a triangular wave, the generation of tsunamis and the propagation of a wave up to overturning. Fluid–structure interaction examples include the free and forced motion of a circular cylinder and the sway, heave and roll motion of a U‐shaped body in a tank with a flap wave generator. The presented examples demonstrate the applicability and performance of the implicit scheme with consistent linearization. Copyright © 2001 John Wiley & Sons. Ltd.     

An adaptive domain decomposition coupled finite element–boundary element method for solving problems in elasto‐plasticity

The purpose of this paper is to present an adaptive finite element–boundary element method (FEM–BEM) coupling method that is valid for both two‐ and three‐dimensional elasto‐plastic analyses. The method takes care of the evolution of the elastic and plastic regions. It eliminates the cumbersome of a trial and error process in the identification of the FEM and BEM sub‐domains in the standard FEM–BEM coupling approaches. The method estimates the FEM and BEM sub‐domains and automatically generates/adapts the FEM and BEM meshes/sub‐domains, according to the state of computation. The results for two‐ and three‐dimensional applications in elasto‐plasticity show the practicality and the efficiency of the adaptive FEM–BEM coupling method. Copyright © 2009 John Wiley & Sons, Ltd.     

ODDLS: A new unstructured mesh finite element method for the analysis of free surface flow problems

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.     

Fully implicit finite element method for the modeling of free surface flows with surface tension effect

A new approach based on the use of the Newton and level set methods allows to follow the motion of interfaces with surface tension immersed in an incompressible Newtonian fluid. Our method features the use of a high‐order fully implicit time integration scheme that circumvents the stability issues related to the explicit discretization of the capillary force when capillary effects dominate. A strategy based on a consistent Newton–Raphson linearization is introduced, and performances are enhanced by using an exact Newton variant that guarantees a third‐order convergence behavior without requiring second‐order derivatives. The problem is approximated by mixed finite elements, while the anisotropic adaptive mesh refinements enable us to increase the computational accuracy. Numerical investigations of the convergence properties and comparisons with benchmark results provide evidence regarding the efficacy of the methodology. The robustness of the method is tested with respect to the standard explicit method, and stability is maintained for significantly larger time steps compared with those allowed by the stability condition. Copyright © 2016 John Wiley & Sons, Ltd.     

An accelerated surface discretization‐based BEM approach for non‐homogeneous linear problems in 3‐D complex domains

For non‐homogeneous or non‐linear problems, a major difficulty in applying the boundary element method (BEM) is the treatment of the volume integrals that arise. An accurate scheme that requires no volume discretization is highly desirable. In this paper, we describe an efficient approach, based on the precorrected‐FFT technique, for the evaluation of volume integrals resulting from non‐homogeneous linear problems. In this approach, the 3‐D uniform grid constructed initially to accelerate surface integration is used as the baseline mesh for the evaluation of volume integrals. As such, no volume discretization of the interior problem domain is necessary. Moreover, with the uniform 3‐D grid, the matrix sparsification techniques (such as the precorrected‐FFT technique used in this work) can be extended to accelerate volume integration in addition to surface integration, thus greatly reducing the computational time. The accuracy and efficiency of our approach are demonstrated through several examples. A 3‐D accelerated BEM solver for Poisson equations has been developed and has been applied to a 3‐D multiply‐connected problem with complex geometries. Good agreement between simulation results and analytical solutions has been obtained. Copyright © 2005 John Wiley & Sons, Ltd.     

A Lagrangian gradient smoothing method for solid‐flow problems using simplicial mesh

A novel Lagrangian gradient smoothing method (L‐GSM) is developed to solve “solid‐flow” (flow media with material strength) problems governed by Lagrangian form of Navier‐Stokes equations. It is a particle‐like method, similar to the smoothed particle hydrodynamics (SPH) method but without the so‐called tensile instability that exists in the SPH since its birth. The L‐GSM uses gradient smoothing technique to approximate the gradient of the field variables, based on the standard GSM that was found working well with Euler grids for general fluids. The Delaunay triangulation algorithm is adopted to update the connectivity of the particles, so that supporting neighboring particles can be determined for accurate gradient approximations. Special techniques are also devised for treatments of 3 types of boundaries: no‐slip solid boundary, free‐surface boundary, and periodical boundary. An advanced GSM operation for better consistency condition is then developed. Tensile stability condition of L‐GSM is investigated through the von Neumann stability analysis as well as numerical tests. The proposed L‐GSM is validated by using benchmarking examples of incompressible flows, including the Couette flow, Poiseuille flow, and 2D shear‐driven cavity. It is then applied to solve a practical problem of solid flows: the natural failure process of soil and the resultant soil flows. The numerical results are compared with theoretical solutions, experimental data, and other numerical results by SPH and FDM to evaluate further L‐GSM performance. It shows that the L‐GSM scheme can give a very accurate result for all these examples. Both the theoretical analysis and the numerical testing results demonstrate that the proposed L‐GSM approach restores first‐order accuracy unconditionally and does not suffer from the tensile instability. It is also shown that the L‐GSM is much more computational efficient compared with SPH, especially when a large number of particles are employed in simulation.     

An effective heuristic for adaptive control of job sequences subject to variation in processing times

Variation in sequential task processing times is common in manufacturing systems. This type of disturbance challenges most scheduling methods since they cannot fundamentally change job sequences to adaptively control production performance as jobs enter the system because actual processing times, are not known in advance. Some research literature indicates that simple rules are more suitable than algorithmic scheduling methods for adaptive control. In this work, a ‘state space – average processing time’ (SS-APT) heuristic is proposed and compared to four most commonly used scheduling rules and two well-established heuristics based on Taillard’s benchmarks. It is shown that the adaptive control is made possible under variation in processing times given the flexibility and strong performance of the SS-APT heuristic, especially for work-in-process inventory control.     

Free‐slip boundary conditions for simulating free‐surface incompressible flows through the particle finite element method

The possibility of using free‐slip conditions within the context of the particle finite element method (PFEM) is investigated. For high Reynolds number engineering applications in which tangential effects at the fluid–solid boundaries are not of primary interest, the use of free‐slip conditions can alleviate the need for very fine boundary layer meshes. Two novel ways for the imposition of free‐slip conditions in the framework of the PFEM are presented. The proposed approach emphasizes robustness and simplicity, while retaining a sufficient level of generality. These two methods are then tested in the case of dam break and sloshing problems, and their respective advantages and drawbacks are discussed. It is also shown how the use of free‐slip conditions can indirectly improve mass conservation properties of the PFEM, even when coarse meshes are employed. Copyright © 2016 John Wiley & Sons, Ltd.     

A 3D Lagrangian gradient smoothing method framework with an adaptable gradient smoothing domain-constructing algorithm for simulating large deformation free surface flows

A novel smoothing particle hydrodynamics (SPH)-like Lagrangian meshfree method, named as Lagrangian gradient smoothing method (L-GSM), has been proposed to avoid the “tensile instability” issue in SPH simulation by replacing the SPH particle-summation gradient approximation technique with a local grid-based GSM gradient smoothing operator. The L-GSM model has been proven effective and efficient when applied to a wide range of large deformation problems for fluids and flowing solids in two-dimensional case. In this study, a three-dimensional (3D) L-GSM numerical framework is proposed for simulating large deformation problems with the existence of free surfaces through developing a widely adaptable 3D gradient smoothing domain (GSD) constructing algorithm. It includes three key novel ingredients: (i) the localized GSD based on an efficient distance-oriented particle-searching algorithm enabling both easy implementation and efficient computation; (ii) a novel algorithm for constructing 3D GSD to guarantee the effectiveness of the 3D GSM gradient operator adaptable to any extreme cases; (iii) a robust normalized 3D GSM gradient operator formulation that can restore the accuracy of gradient approximation even on boundary interface. The effectiveness of the proposed 3D GSD-constructing algorithm is first verified under various distribution conditions of particles. The accuracy of the proposed adaptable 3D GSM gradient algorithm is then examined through conducting a series of numerical experiments with different spacing ratios. Finally, the 3D L-GSM numerical framework is applied to solve a practical problem of free surface flows with large deformation: collapse of a soil column. The results reveal that the present adaptable 3D L-GSM numerical framework can effectively handle the large deformation problems, like flowing solids, with a constantly changing arbitrary free surface profile.     

An enriched finite element method and level sets for axisymmetric two‐phase flow with surface tension

A finite element method for axisymmetric two‐phase flow problems is presented. The method uses an enriched finite element formulation, in which the interface can move arbitrarily through the mesh without remeshing. The enrichment is implemented by the extended finite element method (X‐FEM) which models the discontinuity in the velocity gradient at the interface by a local partition of unity. It provides an accurate representation of the velocity field at interfaces on an Eulerian grid that is not conformal to the weak discontinuity. The interface is represented by a level set which is also used in the construction of the element enrichment. Surface tension effects are considered and the interface curvature is computed from the level set field. The method is demonstrated by several examples. Copyright © 2003 John Wiley & Sons, Ltd.     

A locking‐free selective smoothed finite element method using tetrahedral and triangular elements with adaptive mesh rezoning for large deformation problems

A novel finite element (FE) formulation with adaptive mesh rezoning for large deformation problems is proposed. The proposed method takes the advantage of the selective smoothed FE method (S‐FEM), which has been recently developed as a locking‐free FE formulation with strain smoothing technique. We adopt the selective face‐based smoothed/node‐based smoothed FEM (FS/NS‐FEM‐T4) and edge‐based smoothed/node‐based smoothed FEM (ES/NS‐FEM‐T3) basically but modify them partly so that our method can handle any kind of material constitutive models other than elastic models. We also present an adaptive mesh rezoning method specialized for our S‐FEM formulation with material constitutive models in total form. Because of the modification of the selective S‐FEMs and specialization of adaptive mesh rezoning, our method is locking‐free for severely large deformation problems even with the use of tetrahedral and triangular meshes. The formulation details for static implicit analysis and several examples of analysis of the proposed method are presented in this paper to demonstrate its efficiency. Copyright © 2014 John Wiley & Sons, Ltd.     

An adaptive fixed mesh method for modelling and simulating of unsteady two‐phase flows with sharp physical interfaces

We present in this paper a new computational method for simulation of two‐phase flow problems with moving boundaries and sharp physical interfaces. An adaptive interface‐capturing technique (ICT) of the Eulerian type is developed for capturing the motion of the interfaces (free surfaces) in an unsteady flow state. The adaptive method is mainly based on the relative boundary conditions of the zero pressure head, at which the interface is corresponding to a free surface boundary. The definition of the free surface boundary condition is used as a marker for identifying the position of the interface (free surface) in the two‐phase flow problems. An initial‐value‐problem (IVP) partial differential equation (PDE) is derived from the dynamic conditions of the interface, and it is designed to govern the motion of the interface in time. In this adaptive technique, the Navier–Stokes equations written for two incompressible fluids together with the IVP are solved numerically over the flow domain. An adaptive mass conservation algorithm is constructed to govern the continuum of the fluid. The finite element method (FEM) is used for the spatial discretization and a fully coupled implicit time integration method is applied for the advancement in time. FE‐stabilization techniques are added to the standard formulation of the discretization, which possess good stability and accuracy properties for the numerical solution. The adaptive technique is tested in simulation of some numerical examples. With the test problems presented here, we demonstrated that the adaptive technique is a simple tool for modelling and computation of complex motion of sharp physical interfaces in convection–advection‐dominated flow problems. We also demonstrated that the IVP and the evolution of the interface function are coupled explicitly and implicitly to the system of the computed unknowns in the flow domain. Copyright © 2005 John Wiley & Sons, Ltd.     

An element‐free Galerkin method for 3D crack propagation simulation under complicated stress conditions

This study develops an element‐free Galerkin method based on the moving least‐squares approximation to trace three‐dimensional crack propagation under complicated stress conditions. The crack surfaces are modelled by a collection of planar triangles that are added when cracks propagate. The visibility criterion is adopted to treat the screening effect of the cracks on the influenced domain of a Gaussian point. Cracks are assumed to propagate in the perpendicular planes at crack front points when the strain energy release rates reach the material fracture toughness. This method is unique in that it uses a nonlinear contact iterative algorithm to consider contributions of crack surface interaction to the global equilibrium equations, so that crack opening, sliding and closing under complicated stress states can be efficiently modelled. Two numerical examples of three‐dimensional quasi‐static crack propagation were modelled with satisfactory results. Copyright © 2012 John Wiley & Sons, Ltd.     

Global parameterization of a topological surface defined as a collection of trimmed bi‐parametric patches: Application to automatic mesh construction

We describe a new geometric algorithm to map surfaces into a plane convex area. The mapping transformation is bijective; it redefines the whole surface as a unique bi‐parametric patch. Thus this mapping provides a global parametrization of the surface. The surfaces are issued from industrial CAD software; they are usually described by a large number of patches and there are many shortcomings. Indeed, the decomposition into patches depends on the algorithm of the geometric modelling system used for design and usually has no meaning for any technological application. Moreover, in many cases, the surface definition is not compatible, i.e. patches are not well connected, some patches are self‐intersecting or intersect each other. Many applications are hard to address because of these defects. In this paper we show how patch‐independent meshing techniques may be easily automated using a unique metric in a plane parametric space. Thus we provide an automatic procedure to build valid meshes over free‐form surfaces issued from industrial CAD software (Computer Aided Design: this terminology should refer to a large amount of software. For the scope of this paper we only refer to geometric modelling systems. Indeed geometric modelling systems remain the kernel of many CAD software). Copyright © 2002 John Wiley & Sons, Ltd.     

Numerical analysis of a new Eulerian–Lagrangian finite element method applied to steady‐state hot rolling processes

A finite element code for steady‐state hot rolling processes of rigid–visco‐plastic materials under plane–strain conditions was developed in a mixed Eulerian–Lagrangian framework. This special set up allows for a direct calculation of the local deformations occurring at the free surfaces outside the contact region between the strip and the work roll. It further simplifies the implementation of displacement boundary conditions, such as the impenetrability condition. When applied to different practical hot rolling situations, ranging from thick slab to ultra‐thin strip rolling, the velocity–displacement based model (briefly denoted as vu‐model) in this mixed Eulerian–Lagrangian reference system proves to be a robust and efficient method. The vu‐model is validated against a solely velocity‐based model (vv‐model) and against elementary methods based on the Kármán–Siebel and Orowan differential equations. The latter methods, when calibrated, are known to be in line with experimental results for homogeneous deformation cases. For a massive deformation it is further validated against the commercial finite‐element software package Abaqus/Explicit. It is shown that the results obtained with the vu‐model are in excellent agreement with the predictions of the vv‐model and that the vu‐model is even more robust than its vv‐counterpart. Throughout the study we assumed a rigid cylindrical work roll; only for the homogeneous test case, we also investigated the effect of an elastically deformable work roll within the frame of the Jortner Green's function method. The new modelling approach combines the advantages of conventional Eulerian and Lagrangian modelling concepts and can be extended to three dimensions in a straightforward manner. Copyright © 2004 John Wiley & Sons, Ltd.     

Dimension‐Controllable Microtube Arrays by Dynamic Holographic Processing as 3D Yeast Culture Scaffolds for Asymmetrical Growth Regulation

Transparent microtubes can function as unique cell culture scaffolds, because the tubular 3D microenvironment they provide is very similar to the narrow space of capillaries in vivo. However, how to realize the fabrication of microtube‐arrays with variable cross‐section dynamically remains challenging. Here, a dynamic holographic processing method for producing high aspect ratio (≈20) microtubes with tunable outside diameter (6–16 µm) and inside diameter (1–10 µm) as yeast culture scaffolds is reported. A ring‐structure Bessel beam is modulated from a typical Gaussian‐distributed femtosecond laser beam by a spatial light modulator. By combining the axial scanning of the focused beam and the dynamic display of holograms, dimension‐controllable microtube arrays (straight, conical, and drum‐shape) are rapidly produced by two‐photon polymerization. The outside and inside diameters, tube heights, and spatial arrangements are readily tuned by loading different computer‐generated holograms and changing the processing parameters. The transparent microtube array as a nontrivial tool for capturing and culturing the budding yeasts reveals the significant effect of tube diameter on budding characteristics. In particular, the conical tube with the inside diameter varying from 5 to 10 µm has remarkable asymmetrical regulation on the growth trend of captured yeasts.     

A parallel Galerkin boundary element method for surface radiation and mixed heat transfer calculations in complex 3‐D geometries

This paper presents a parallel Galerkin boundary element method for the solution of surface radiation exchange problems and its coupling with the finite element method for mixed mode heat transfer computations in general 3‐D geometries. The computational algorithm for surface radiation calculations is enhanced with the implementation of ideas used for 3‐D computer graphics applications and with data structure management involving creating and updating various element lists optimized for numerical performance. The algorithm for detecting the internal third party blockages of thermal rays is presented, which involves a four‐step procedure, i.e. the primary clip, secondary clip and adaptive integration with checking. Case studies of surface radiation and mixed heat transfer in both simple and complex 3‐D geometric configurations are presented. It is found that a majority of computational time is spent on the detection of foreign element blockages and parallel computing is ideally suited for surface radiation calculations. Results show that the decrease of the CPU time approaches asymptotically to an inverse rule for parallel computing of surface radiation exchanges. For large‐scale computations involving complex 3‐D geometries, an iterative procedure is a preferred approach for the coupling of the Galerkin boundary and finite elements for mixed mode heat transfer calculations. Copyright © 2004 John Wiley & Sons, Ltd.