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Interface Conditions (interface + condition)
Selected AbstractsA mass-conserving Level-Set method for modelling of multi-phase flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2005S. P. van der Pijl Abstract A mass-conserving Level-Set method to model bubbly flows is presented. The method can handle high density-ratio flows with complex interface topologies, such as flows with simultaneous occurrence of bubbles and droplets. Aspects taken into account are: a sharp front (density changes abruptly), arbitrarily shaped interfaces, surface tension, buoyancy and coalescence of droplets/bubbles. Attention is paid to mass-conservation and integrity of the interface. The proposed computational method is a Level-Set method, where a Volume-of-Fluid function is used to conserve mass when the interface is advected. The aim of the method is to combine the advantages of the Level-Set and Volume-of-Fluid methods without the disadvantages. The flow is computed with a pressure correction method with the Marker-and-Cell scheme. Interface conditions are satisfied by means of the continuous surface force methodology and the jump in the density field is maintained similar to the ghost fluid method for incompressible flows. Copyright © 2005 John Wiley & Sons, Ltd. [source] Semi-coupled air/water immersed boundary approach for curvilinear dynamic overset grids with application to ship hydrodynamicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2008Juntao Huang Abstract For many problems in ship hydrodynamics, the effects of air flow on the water flow are negligible (the frequently called free surface conditions), but the air flow around the ship is still of interest. A method is presented where the water flow is decoupled from the air solution, but the air flow uses the unsteady water flow as a boundary condition. The authors call this a semi-coupled air/water flow approach. The method can be divided into two steps. At each time step the free surface water flow is computed first with a single-phase method assuming constant pressure and zero stress on the interface. The second step is to compute the air flow assuming the free surface as a moving immersed boundary (IB). The IB method developed for Cartesian grids (Annu. Rev. Fluid Mech. 2005; 37:239,261) is extended to curvilinear grids, where no-slip and continuity conditions are used to enforce velocity and pressure boundary conditions for the air flow. The forcing points close to the IB can be computed and corrected under a sharp interface condition, which makes the computation very stable. The overset implementation is similar to that of the single-phase solver (Comput. Fluids 2007; 36:1415,1433), with the difference that points in water are set as IB points even if they are fringe points. Pressure,velocity coupling through pressure implicit with splitting of operators or projection methods is used for water computations, and a projection method is used for the air. The method on each fluid is a single-phase method, thus avoiding ill-conditioned numerical systems caused by large differences of fluid properties between air and water. The computation is only slightly slower than the single-phase version, with complete absence of spurious velocity oscillations near the free surface, frequently present in fully coupled approaches. Validations are performed for laminar Couette flow over a wavy boundary by comparing with the analytical solution, and for the surface combatant model David Taylor Model Basin (DTMB) 5512 by comparing with Experimental Fluid Dynamics (EFD) and the results of two-phase level set computations. Complex flow computations are demonstrated for the ONR Tumblehome DTMB 5613 with superstructure subject to waves and wind, including 6DOF motions and broaching in SS7 irregular waves and wind. Copyright © 2008 John Wiley & Sons, Ltd. [source] Two singular point linear Hamiltonian systems with an interface conditionMATHEMATISCHE NACHRICHTEN, Issue 3 2010Horst Behncke Abstract We consider the problem of a linear Hamiltionian system on , with an interface condition which we take to be at x = 0. Assuming limit point conditions at ±,, we prove the problem is uniquely solvable, and a resolvent is constructed. Our method of solution is to map the problem onto a half line problem of double size and apply the theory of half line problems. A Titchmarsh-Weyl function is associated with the problem, and a unitary transform is constructed which maps the differential operator onto the multiplication operator in the Hilbert space determined by the spectral function , (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] A discontinuous Galerkin method for elliptic interface problems with application to electroporationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2009Grégory Guyomarc'h Abstract We solve elliptic interface problems using a discontinuous Galerkin (DG) method, for which discontinuities in the solution and in its normal derivatives are prescribed on an interface inside the domain. Standard ways to solve interface problems with finite element methods consist in enforcing the prescribed discontinuity of the solution in the finite element space. Here, we show that the DG method provides a natural framework to enforce both discontinuities weakly in the DG formulation, provided the triangulation of the domain is fitted to the interface. The resulting discretization leads to a symmetric system that can be efficiently solved with standard algorithms. The method is shown to be optimally convergent in the L2 -norm. We apply our method to the numerical study of electroporation, a widely used medical technique with applications to gene therapy and cancer treatment. Mathematical models of electroporation involve elliptic problems with dynamic interface conditions. We discretize such problems into a sequence of elliptic interface problems that can be solved by our method. We obtain numerical results that agree with known exact solutions. Copyright © 2008 John Wiley & Sons, Ltd. [source] The immersed/fictitious element method for fluid,structure interaction: Volumetric consistency, compressibility and thin membersINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2008Hongwu Wang Abstract A weak form and an implementation are given for fluid,structure interaction by the immersed/fictitious element method for compressible fluids. The weak form is applicable to models where the fluid is described by Eulerian coordinates while the solid is described by Lagrangian coordinates, which suits their intrinsic characteristics. A unique feature of the method is the treatment of the fictitious fluid by a Lagrangian description, which simplifies the interface conditions. Methods for enforcing volumetric consistency between the fluid and solid and treating thin members are given. Although a compressible viscous fluid is considered here, the new developments can be applied to incompressible fluids. Copyright © 2007 John Wiley & Sons, Ltd. [source] Hydroelastic vibrations of flexible rectangular tanks partially filled with liquidINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2007Ding Zhou Abstract In this paper, the three-dimensional vibratory characteristics of flexible rectangular tanks partially filled with liquid are studied. The surface waves of the liquid are taken into account in the analysis. Both the bulging modes of the tank-wall vibration and the sloshing modes of the liquid oscillation are investigated. The vibrating modes of the liquid,tank system are divided into four distinct categories: double symmetric modes (SS); antisymmetric,symmetric modes (AS); symmetric,antisymmetric modes (SA) and double antisymmetric modes (AA). Each of these categories is separately investigated. The velocity potential of the liquid is analytically deduced by using a combination of the superposition method and the method of separation of variables. According to the liquid,tank interface conditions and the orthogonality of trigonometric functions, the coefficients in the solution of liquid velocity potential are expressed in the integral forms including the tank,wall dynamic deflection. A set of reasonable static beam functions is constructed as the admissible functions of the tank-wall vibration. The eigenfrequency equation of the liquid,tank system is derived by using a combination of the Rayleigh,Ritz method and the Galerkin method. Convergence study demonstrates the high accuracy and small computational cost of the proposed approach. Finally, some numerical results are presented for the first time. Copyright © 2006 John Wiley & Sons, Ltd. [source] Automatic energy conserving space,time refinement for linear dynamic structural problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2005P. Cavin Abstract In this paper a local space,time automatic refinement method (STAR method) is developed to efficiently solve time-dependent problems using FEM techniques. The automatic process is driven by an energy or a displacement error indicator which controls the precision of the result. The STAR method solves the numerical problem on grids with different mesh size. For the Newmark schemes, a general demonstration, using the energy method, gives the interface conditions between two successive grids which is compatible with the stability of the scheme. Finally, using a linear one-dimensional example, the convergence of the method and the precision of the results are discussed. Copyright © 2005 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] Optimal convergence properties of the FETI domain decomposition methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2007Y. Maday Abstract In this paper an original variant of the FETI domain decomposition method is introduced for heterogeneous media. This method uses new absorbing interface conditions in place of the Neumann interface conditions defined in the classical FETI method. The optimal convergence properties of the classical FETI method and of its variant are first demonstrated, both in the case of homogeneous and heterogeneous media. Secondly, novel and efficient absorbing interface conditions, which avoid rigid body motions, are investigated and analysed. Numerical experiments illustrate the dependence of the proposed method upon several parameters, and confirm the robustness and efficiency of this method when equipped with such absorbing interface conditions. Copyright © 2006 John Wiley & Sons, Ltd. [source] A subdomain boundary element method for high-Reynolds laminar flow using stream function-vorticity formulationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2004Matja Abstract The paper presents a new formulation of the integral boundary element method (BEM) using subdomain technique. A continuous approximation of the function and the function derivative in the direction normal to the boundary element (further ,normal flux') is introduced for solving the general form of a parabolic diffusion-convective equation. Double nodes for normal flux approximation are used. The gradient continuity is required at the interior subdomain corners where compatibility and equilibrium interface conditions are prescribed. The obtained system matrix with more equations than unknowns is solved using the fast iterative linear least squares based solver. The robustness and stability of the developed formulation is shown on the cases of a backward-facing step flow and a square-driven cavity flow up to the Reynolds number value 50 000. Copyright © 2004 John Wiley & Sons, Ltd. [source] Glass Transition of Low-Dimensional PolystyreneMACROMOLECULAR RAPID COMMUNICATIONS, Issue 7 2004Qing Jiang Abstract Summary: A unified model is developed for the finite size-effect on the glass-transition temperature of polymers, Tg(D), where D denotes the diameter of particles or thickness of films. In terms of this model, Tg depends on both the size and interface conditions. The predicted results are consistent with the experimental evidence for polystyrene (PS) particles and films with different interface situations. Tg(D) function of free-standing PS films. [source] Heat transfer in composite materials with Stefan,Boltzmann interface conditionsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 11 2008Yang Gufan Abstract In this paper, we discuss nonstationary heat transfer problems in composite materials. This problem can be formulated as the parabolic equation with Stefan,Boltzmann interface conditions. It is proved that there exists a unique global classical solution to one-dimensional problems. Moreover, we propose a numerical algorithm by the finite difference method for this nonlinear transmission problem. Copyright © 2007 John Wiley & Sons, Ltd. [source] Unified finite element discretizations of coupled Darcy,Stokes flowNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2009Trygve Karper Abstract In this article, we discuss some new finite element methods for flows which are governed by the linear stationary Stokes system on one part of the domain and by a second order elliptic equation derived from Darcy's law in the rest of the domain, and where the solutions in the two domains are coupled by proper interface conditions. All the methods proposed here utilize the same finite element spaces on the entire domain. In particular, we show how the coupled problem can be solved by using standard Stokes elements like the MINI element or the Taylor,Hood element in the entire domain. Furthermore, for all the methods the handling of the interface conditions are straightforward. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 [source] Thermal conductance of the AlN/Si and AlN/SiC interfaces calculated with taking into account the detailed phonon spectra of the materials and the interface conditionsPHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 1 2010M. Kazan Abstract We present a calculation of the thermal conductance (TC) of the interface between aluminium nitride (AlN) and silicon (Si) and that between AlN and silicon carbide (SiC) with taking into account the detailed phonon spectra of the materials, as obtained from first principles calculations, and the interface conditions. On the basis of the results obtained, we discuss the relation between the interface TC, the interface conditions, and the mismatches between the acoustic waves velocities and the phonon densities of states of the materials in contact. Our calculation method is expected to provide a reliable tool for thermal management strategy, independently from the substrate choice (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Coupling Techniques for Thermal and Mechanical Fluid-Structure-Interactions in AeronauticsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2005Matthias Haupt For the coupled thermal and mechanical analysis of spacecraft structures a simulation environment was developed containing the necessary coupling techniques. The numerical concept uses the weak form of the interface conditions on the coupling surface. The iterative solution of the coupled equations is based on the classical Dirichlet-Neumann approach. Transient problems are handled with iterative staggered schemes. A flexible component-based software environment combines existing fluid and structural analysis codes. Aspects of the architecture and its implementation are described. Finally an application to a spacecraft structure is shown. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Ginzburg,Landau equations and boundary conditions for superconductors in static magnetic fieldsANNALEN DER PHYSIK, Issue 5 2005J. Bünemann Abstract We derive the Ginzburg,Landau equations for superconductors in static magnetic fields. Instead of the square of the gauge-invariant gradient of the order-parameter wave function, we consider the quantum-mechanical expression for the kinetic energy in the Ginzburg,Landau energy functional. We introduce a new surface term in the free energy functional which results in the de Gennes interface conditions. The phenomenological Ginzburg,Landau theory thus contains three length scales which must be determined from microscopic theory: the Ginzburg,Landau coherence length, the London penetration depth, and the de Gennes length. [source] | ||||||||||||||||