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Moving Boundaries (moving + boundary)

Distribution by Scientific Domains
Engineering84%

Terms modified by Moving Boundaries

  • moving boundary problem
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    Selected Abstracts

    System zones in capillary zone electrophoresis: Moving boundaries caused by freely migrating hydrogen ions

    ELECTROPHORESIS, Issue 2 2005
    Jozef L. Beckers
    Abstract We demonstrate that system zones (SZs) can be expected in background electrolytes (BGEs) with a low buffer capacity. The mobilities of this type of SZ (mSZ) could be determined by calculations both based on a mathematical model and by a simulation program. The values of mSZ are increasing for decreasing buffer capacities and lower concentrations of the BGEs. For completely unbuffered BGEs with a pH below 7, the mSZ reached values up to 350×10,9 m2V,1s,1. This value indicates that the existence of this type of SZ originates from migrating hydrogen ions. Although both the mathematical model and simulation program do not consider the influence of the pH of the sample solution, experiments have shown that the pH of the sample solution is also very important. The lower the pH of the sample solution, the larger the mSZ in a specific BGE for cationic SZs. Using completely unbuffered BGEs the hydrogen ions present in the original sample start to migrate freely through the capillary tube with the mobility of a single hydrogen ion and cause stepwise disturbances in the base line of the detector trace. It is remarkable that this type of SZ appears not to affect the electromigration dispersion (EMD) in a strong way and so far only dips could be obtained experimentally. [source]

    A hybrid immersed boundary and material point method for simulating 3D fluid,structure interaction problems

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2008
    Anvar Gilmanov
    Abstract A numerical method is developed for solving the 3D, unsteady, incompressible Navier,Stokes equations in curvilinear coordinates containing immersed boundaries (IBs) of arbitrary geometrical complexity moving and deforming under forces acting on the body. Since simulations of flow in complex geometries with deformable surfaces require special treatment, the present approach combines a hybrid immersed boundary method (HIBM) for handling complex moving boundaries and a material point method (MPM) for resolving structural stresses and movement. This combined HIBM & MPM approach is presented as an effective approach for solving fluid,structure interaction (FSI) problems. In the HIBM, a curvilinear grid is defined and the variable values at grid points adjacent to a boundary are forced or interpolated to satisfy the boundary conditions. The MPM is used for solving the equations of solid structure and communicates with the fluid through appropriate interface-boundary conditions. The governing flow equations are discretized on a non-staggered grid layout using second-order accurate finite-difference formulas. The discrete equations are integrated in time via a second-order accurate dual time stepping, artificial compressibility scheme. Unstructured, triangular meshes are employed to discretize the complex surface of the IBs. The nodes of the surface mesh constitute a set of Lagrangian control points used for tracking the motion of the flexible body. The equations of the solid body are integrated in time via the MPM. At every instant in time, the influence of the body on the flow is accounted for by applying boundary conditions at stationary curvilinear grid nodes located in the exterior but in the immediate vicinity of the body by reconstructing the solution along the local normal to the body surface. The influence of the fluid on the body is defined through pressure and shear stresses acting on the surface of the body. The HIBM & MPM approach is validated for FSI problems by solving for a falling rigid and flexible sphere in a fluid-filled channel. The behavior of a capsule in a shear flow was also examined. Agreement with the published results is excellent. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    A new modification of the immersed-boundary method for simulating flows with complex moving boundaries

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2006
    Jian Deng
    Abstract In this paper, a new immersed-boundary method for simulating flows over complex immersed, moving boundaries is presented. The flow is computed on a fixed Cartesian mesh and the solid boundaries are allowed to move freely through the mesh. The present method is based on a finite-difference approach on a staggered mesh together with a fractional-step method. It must be noted that the immersed boundary is generally not coincident with the position of the solution variables on the grid, therefore, an appropriate strategy is needed to construct a relationship between the curved boundary and the grid points nearby. Furthermore, a momentum forcing is added on the body boundaries and also inside the body to satisfy the no-slip boundary condition. The immersed boundary is represented by a series of interfacial markers, and the markers are also used as Lagrangian forcing points. A linear interpolation is then used to scale the Lagrangian forcing from the interfacial markers to the corresponding grid points nearby. This treatment of the immersed-boundary is used to simulate several problems, which have been validated with previous experimental results in the open literature, verifying the accuracy of the present method. Copyright © 2006 John Wiley & Sons, Ltd. [source]

    A particle finite element method applied to long wave run-up

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2006
    J. Birknes
    Abstract This paper presents a Lagrangian,Eulerian finite element formulation for solving fluid dynamics problems with moving boundaries and employs the method to long wave run-up. The method is based on a set of Lagrangian particles which serve as moving nodes for the finite element mesh. Nodes at the moving shoreline are identified by the alpha shape concept which utilizes the distance from neighbouring nodes in different directions. An efficient triangulation technique is then used for the mesh generation at each time step. In order to validate the numerical method the code has been compared with analytical solutions and a preexisting finite difference model. The main focus of our investigation is to assess the numerical method through simulations of three-dimensional dam break and long wave run-up on curved beaches. Particularly the method is put to test for cases where different shoreline segments connect and produce a computational domain surrounding dry regions. Copyright © 2006 John Wiley & Sons, Ltd. [source]

    Flow simulation on moving boundary-fitted grids and application to fluid,structure interaction problems

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2006
    Martin Engel
    Abstract We present a method for the parallel numerical simulation of transient three-dimensional fluid,structure interaction problems. Here, we consider the interaction of incompressible flow in the fluid domain and linear elastic deformation in the solid domain. The coupled problem is tackled by an approach based on the classical alternating Schwarz method with non-overlapping subdomains, the subproblems are solved alternatingly and the coupling conditions are realized via the exchange of boundary conditions. The elasticity problem is solved by a standard linear finite element method. A main issue is that the flow solver has to be able to handle time-dependent domains. To this end, we present a technique to solve the incompressible Navier,Stokes equation in three-dimensional domains with moving boundaries. This numerical method is a generalization of a finite volume discretization using curvilinear coordinates to time-dependent coordinate transformations. It corresponds to a discretization of the arbitrary Lagrangian,Eulerian formulation of the Navier,Stokes equations. Here the grid velocity is treated in such a way that the so-called Geometric Conservation Law is implicitly satisfied. Altogether, our approach results in a scheme which is an extension of the well-known MAC-method to a staggered mesh in moving boundary-fitted coordinates which uses grid-dependent velocity components as the primary variables. To validate our method, we present some numerical results which show that second-order convergence in space is obtained on moving grids. Finally, we give the results of a fully coupled fluid,structure interaction problem. It turns out that already a simple explicit coupling with one iteration of the Schwarz method, i.e. one solution of the fluid problem and one solution of the elasticity problem per time step, yields a convergent, simple, yet efficient overall method for fluid,structure interaction problems. Copyright © 2005 John Wiley & Sons, Ltd. [source]

    Study of particle trajectories, residence times and flow behavior in kneading discs of intermeshing co-rotating twin-screw extruders

    POLYMER ENGINEERING & SCIENCE, Issue 4 2004
    V. L. Bravo
    A three-dimensional finite element model was implemented for the solution of mass and momentum conservation equations in the kneading disc section of an intermeshing co-rotating twin-screw extruder. The polymer melt was modeled with a Carreau constitutive equation. The particle tracking technique was used to obtain residence times and analyze distributive mixing for different length to diameter ratios (L/D) of kneading discs. Previous studies from Kalyon et al. (1) and Cheng and Manas-Zloczower (2) have shown that the mixing performance of intermeshing co-rotating twin-screw extruders is highly dependent on the combination of screw configuration and operating conditions. The complexity of the geometry and the transient character of the flow demand powerful computational tools to characterize the flow and to develop a prediction tool for the analysis of relative performance between different configurations. Difficulties arise in the particle tracking technique because of the time discretization and the presence of moving boundaries. Results show the importance of particle history on the evaluation of the relative performance of different configurations of kneading blocks and suggest a reevaluation of the use of average flow characteristics for the analysis of mixing. Results also confirm the importance of an accurate description of the geometry and clearances in order to obtain information about relative mixing performance. Polym. Eng. Sci. 44:779,793, 2004. © 2004 Society of Plastics Engineers. [source]

    Numerical solution of the oxygen diffusion in absorbing tissue with a moving boundary

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 9 2006
    Abdellatif BoureghdaArticle first published online: 9 FEB 200
    Abstract A problem of oxygen diffusion in absorbing medium is complex. A mathematical model of this problem is presented, which has previously been investigated by Crank and Gupta (J. Inst. Math. Appl. 1972; 10: 19,33) is studied using a different method of solution. Approximate analytical and numerical solutions of its partial differential equations are obtained, which describe the diffusion of oxygen in absorbing tissue. A moving boundary is an essential feature of this problem but the conditions which determine its movements are different. The results are compared with those of Crank and Gupta. In most cases the agreement is fair. Copyright © 2006 John Wiley & Sons, Ltd. [source]

    Starting solutions for the boundary immobilization method

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 6 2005
    J. Caldwell
    Abstract The boundary immobilization method (BIM) is extended to the cases of outward spherical and cylindrical solidifications, which involves the development of starting solutions. When applying the method to time-dependent problems, good agreement is achieved when comparing the positions of the moving boundary and the temperature distribution with those obtained by the perturbation method. Copyright © 2004 John Wiley & Sons, Ltd. [source]

    Numerical modelling of chemical effects of magma solidification problems in porous rocks

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2005
    Chongbin Zhao
    Abstract The solidification of intruded magma in porous rocks can result in the following two consequences: (1) the heat release due to the solidification of the interface between the rock and intruded magma and (2) the mass release of the volatile fluids in the region where the intruded magma is solidified into the rock. Traditionally, the intruded magma solidification problem is treated as a moving interface (i.e. the solidification interface between the rock and intruded magma) problem to consider these consequences in conventional numerical methods. This paper presents an alternative new approach to simulate thermal and chemical consequences/effects of magma intrusion in geological systems, which are composed of porous rocks. In the proposed new approach and algorithm, the original magma solidification problem with a moving boundary between the rock and intruded magma is transformed into a new problem without the moving boundary but with the proposed mass source and physically equivalent heat source. The major advantage in using the proposed equivalent algorithm is that a fixed mesh of finite elements with a variable integration time-step can be employed to simulate the consequences and effects of the intruded magma solidification using the conventional finite element method. The correctness and usefulness of the proposed equivalent algorithm have been demonstrated by a benchmark magma solidification problem. Copyright © 2005 John Wiley & Sons, Ltd. [source]

    Numerical solution of steady free-surface flows by the adjoint optimal shape design method

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2003
    E. H. van Brummelen
    Abstract Numerical solution of flows that are partially bounded by a freely moving boundary is of great importance in practical applications such as ship hydrodynamics. Free-boundary problems can be reformulated into optimal shape design problems, which can in principle be solved efficiently by the adjoint method. In this work we investigate the suitability of the adjoint shape optimization method for solving steady free-surface flows. The asymptotic convergence behaviour of the method is determined for free-surface flows in 2D and 3D. It is shown that the convergence behaviour depends sensitively on the occurrence of critical modes. The convergence behaviour is moreover shown to be mesh-width independent, provided that proper preconditioning is applied. Numerical results are presented for 2D flow over an obstacle in a channel. The observed convergence behaviour is indeed mesh-width independent and conform the derived asymptotic estimates. Copyright © 2003 John Wiley & Sons, Ltd. [source]

    2-D transmitral flows simulation by means of the immersed boundary method on unstructured grids

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2002
    F. M. Denaro
    Abstract Interaction between computational fluid dynamics and clinical researches recently allowed a deeper understanding of the physiology of complex phenomena involving cardio-vascular mechanisms. The aim of this paper is to develop a simplified numerical model based on the Immersed Boundary Method and to perform numerical simulations in order to study the cardiac diastolic phase during which the left ventricle is filled with blood flowing from the atrium throughout the mitral valve. As one of the diagnostic problems to be faced by clinicians is the lack of a univocal definition of the diastolic performance from the velocity measurements obtained by Eco,Doppler techniques, numerical simulations are supposed to provide an insight both into the physics of the diastole and into the interpretation of experimental data. An innovative application of the Immersed Boundary Method on unstructured grids is presented, fulfilling accuracy requirements related to the development of a thin boundary layer along the moving immersed boundary. It appears that this coupling between unstructured meshes and the Immersed Boundary Method is a promising technique when a wide range of spatial scales is involved together with a moving boundary. Numerical simulations are performed in a range of physiological parameters and a qualitative comparison with experimental data is presented, in order to demonstrate that, despite the simplified model, the main physiological characteristics of the diastole are well represented. Copyright © 2002 John Wiley & Sons, Ltd. [source]