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Level Set Method (level + set_method)
Selected AbstractsTransport and deformation of droplets in a microdevice using dielectrophoresisELECTROPHORESIS, Issue 4 2007Pushpendra Singh Professor Abstract In microfluidic devices the fluid can be manipulated either as continuous streams or droplets. The latter is particularly attractive as individual droplets can not only move but also split and fuse, thus offering great flexibility for applications such as laboratory-on-a-chip. We consider the transport of liquid drops immersed in a surrounding liquid by means of the dielectrophoretic force generated by electrodes mounted at the bottom of a microdevice. The direct numerical simulation (DNS) approach is used to study the motion of droplets subjected to both hydrodynamic and electrostatic forces. Our technique is based on a finite element scheme using the fundamental equations of motion for both the droplets and surrounding fluid. The interface is tracked by the level set method and the electrostatic forces are computed using the Maxwell stress tensor. The DNS results show that the droplets move, and deform, under the action of nonuniform electric stresses on their surfaces. The deformation increases as the drop moves closer to the electrodes. The extent to which the isolated drops deform depends on the electric Weber number. When the electric Weber number is small, the drops remain spherical; otherwise, the drops stretch. Two droplets, however, that are sufficiently close to each other, can deform and coalesce, even if the electric Weber number is small. This phenomenon does not rely on the magnitude of the electric stresses generated by the bulk electric field, but instead is due to the attractive electrostatic drop,drop interaction overcoming the surface tension force. Experimental results are also presented and found to be in agreement with the DNS results. [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 structural optimization method based on the level set method using a new geometry-based re-initialization schemeINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2010Shintaro Yamasaki Abstract Structural optimization methods based on the level set method are a new type of structural optimization method where the outlines of target structures can be implicitly represented using the level set function, and updated by solving the so-called Hamilton,Jacobi equation based on a Eulerian coordinate system. These new methods can allow topological alterations, such as the number of holes, during the optimization process whereas the boundaries of the target structure are clearly defined. However, the re-initialization scheme used when updating the level set function is a critical problem when seeking to obtain appropriately updated outlines of target structures. In this paper, we propose a new structural optimization method based on the level set method using a new geometry-based re-initialization scheme where both the numerical analysis used when solving the equilibrium equations and the updating process of the level set function are performed using the Finite Element Method. The stiffness maximization, eigenfrequency maximization, and eigenfrequency matching problems are considered as optimization problems. Several design examples are presented to confirm the usefulness of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd. [source] A finite element-based level set method for structural optimizationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2010Xianghua Xing Abstract A finite element-based level set method is implemented for structural optimization. The streamline diffusion finite element method is used for solving both the level set equation and the reinitialization equation. The lumped scheme is addressed and the accuracy is compared with the conventional finite difference-based level set method. A Dirichlet boundary condition is enforced during the reinitialization to prevent the boundary from drifting. Numerical examples of minimum mean compliance design illustrate the reliability of the proposed optimization method. Copyright © 2009 John Wiley & Sons, Ltd. [source] Piecewise constant level set method for structural topology optimizationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2009Peng Wei Abstract In this paper, a piecewise constant level set (PCLS) method is implemented to solve a structural shape and topology optimization problem. In the classical level set method, the geometrical boundary of the structure under optimization is represented by the zero level set of a continuous level set function, e.g. the signed distance function. Instead, in the PCLS approach the boundary is described by discontinuities of PCLS functions. The PCLS method is related to the phase-field methods, and the topology optimization problem is defined as a minimization problem with piecewise constant constraints, without the need of solving the Hamilton,Jacobi equation. The result is not moving the boundaries during the iterative procedure. Thus, it offers some advantages in treating geometries, eliminating the reinitialization and naturally nucleating holes when needed. In the paper, the PCLS method is implemented with the additive operator splitting numerical scheme, and several numerical and procedural issues of the implementation are discussed. Examples of 2D structural topology optimization problem of minimum compliance design are presented, illustrating the effectiveness of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd. [source] An assumed-gradient finite element method for the level set equationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2005Hashem M. Mourad Abstract The level set equation is a non-linear advection equation, and standard finite-element and finite-difference strategies typically employ spatial stabilization techniques to suppress spurious oscillations in the numerical solution. We recast the level set equation in a simpler form by assuming that the level set function remains a signed distance to the front/interface being captured. As with the original level set equation, the use of an extensional velocity helps maintain this signed-distance function. For some interface-evolution problems, this approach reduces the original level set equation to an ordinary differential equation that is almost trivial to solve. Further, we find that sufficient accuracy is available through a standard Galerkin formulation without any stabilization or discontinuity-capturing terms. Several numerical experiments are conducted to assess the ability of the proposed assumed-gradient level set method to capture the correct solution, particularly in the presence of discontinuities in the extensional velocity or level-set gradient. We examine the convergence properties of the method and its performance in problems where the simplified level set equation takes the form of a Hamilton,Jacobi equation with convex/non-convex Hamiltonian. Importantly, discretizations based on structured and unstructured finite-element meshes of bilinear quadrilateral and linear triangular elements are shown to perform equally well. Copyright © 2005 John Wiley & Sons, Ltd. [source] On surface tension modelling using the level set methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2009Sergey V. Shepel Abstract The paper describes and compares the performance of two options for numerically representing the surface tension force in combination with the level set interface-tracking method. In both models, the surface tension is represented as a body force, concentrated near the interface, but the technical implementation is different: the first model is based on a traditional level set approach in which the force is distributed in a band around the interface using a regularized delta function, whereas in the second, the force is partly distributed in a band around the interface and partly localized to the actual computational cells containing the interface. A comparative study, involving analysis of several two-phase flows with moving interfaces, shows that in general the two surface tension models produce results of similar accuracy. However, in the particular case of merging and pinching-off of interfaces, the traditional level set model of surface tension produces an error that results in non-converging solutions for film-like interfaces (i.e. ones involving large contact areas). In contrast, the second model, based on the localized representation of the surface tension force, displays consistent first-order convergence. Copyright © 2008 John Wiley & Sons, Ltd. [source] Coupled ghost fluid/two-phase level set method for curvilinear body-fitted gridsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2007Juntao Huang Abstract A coupled ghost fluid/two-phase level set method to simulate air/water turbulent flow for complex geometries using curvilinear body-fitted grids is presented. The proposed method is intended to treat ship hydrodynamics problems. The original level set method for moving interface flows was based on Heaviside functions to smooth all fluid properties across the interface. We call this the Heaviside function method (HFM). The HFM requires fine grids across the interface. The ghost fluid method (GFM) has been designed to explicitly enforce the interfacial jump conditions, but the implementation of the jump conditions in curvilinear grids is intricate. To overcome these difficulties a coupled GFM/HFM method was developed in which approximate jump conditions are derived for piezometric pressure and velocity and pressure gradients based on exact continuous velocity and stress and jump in momentum conditions with the jump in density maintained but continuity of the molecular and turbulent viscosities imposed. The implementation of the ghost points is such that no duplication of memory storage is necessary. The level set method is adopted to locate the air/water interface, and a fast marching method was implemented in curvilinear grids to reinitialize the level set function. Validations are performed for three tests: super- and sub-critical flow without wave breaking and an impulsive plunging wave breaking over 2D submerged bumps, and the flow around surface combatant model DTMB 5512. Comparisons are made against experimental data, HFM and single-phase level set computations. The proposed method performed very well and shows great potential to treat complicated turbulent flows related to ship flows. Copyright © 2007 John Wiley & Sons, Ltd. [source] A semi-Lagrangian level set method for incompressible Navier,Stokes equations with free surfaceINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2005Leo Miguel González Gutiérrez Abstract In this paper, we formulate a level set method in the framework of finite elements-semi-Lagrangian methods to compute the solution of the incompressible Navier,Stokes equations with free surface. In our formulation, we use a quasi-monotone semi-Lagrangian scheme, which is both unconditionally stable and essentially non oscillatory, to compute the advective terms in the Navier,Stokes equations, the transport equation and the equation of the reinitialization stage for the level set function. The method we propose is quite robust and flexible with regard to the mesh and the geometry of the domain, as well as the magnitude of the Reynolds number. We illustrate the performance of the method in several examples, which range from a benchmark problem to test the volume conservation property of the method to the flow past a NACA0012 foil at high Reynolds number. Copyright © 2005 John Wiley & Sons, Ltd. [source] A level set characteristic Galerkin finite element method for free surface flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2005Ching-Long Lin Abstract This paper presents a numerical method for free surface flows that couples the incompressible Navier,Stokes equations with the level set method in the finite element framework. The implicit characteristic-Galerkin approximation together with the fractional four-step algorithm is employed to discretize the governing equations. The schemes for solving the level set evolution and reinitialization equations are verified with several benchmark cases, including stationary circle, rotation of a slotted disk and stretching of a circular fluid element. The results are compared with those calculated from the level set finite volume method of Yue et al. (Int. J. Numer. Methods Fluids 2003; 42:853,884), which employed the third-order essentially non-oscillatory (ENO) schemes for advection of the level set function in a generalized curvilinear coordinate system. The comparison indicates that the characteristic Galerkin approximation of the level set equations yields more accurate solutions. The second-order accuracy of the Navier,Stokes solver is confirmed by simulation of decay vortex. The coupled system of the Navier,Stokes and level set equations then is validated by solitary wave and broken dam problems. The simulation results are in excellent agreement with experimental data. Copyright © 2005 John Wiley & Sons, Ltd. [source] Numerical analysis of deformed free surface under AC magnetic fieldsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2004Haruhiko Kohno Abstract A novel numerical scheme for the analysis of large deformation of electrically conducting liquid under alternating current magnetic fields is presented. The main features are characterized by two numerical tools; the level set method to calculate deformed free surface stably and the hybrid finite element method and boundary element method to discretize the electromagnetic field efficiently. Two-dimensional numerical simulation of conducting drop deformation is carried out to demonstrate the effectiveness of the present scheme, and the oscillatory behaviour, which depends on the magnitude of surface tension and Lorentz force, is investigated. Copyright © 2004 John Wiley & Sons, Ltd. [source] Adaptive grid based on geometric conservation law level set method for time dependent PDENUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 3 2009Ali R. Soheili Abstract A new method for mesh generation is formulated based on the level set functions, which are solutions of the standard level set evolution equation with the Cartesian coordinates as initial values (Liao et al. J Comput Phys 159 (2000), 103,122; Osher and Sethian J Comput Phys 79 (1988), 12; Sethian, Level set methods and fast marching methods, Cambridge University Press, 1999; Di et al. J Sci Comput 31 (2007), 75,98). The intersection of the level contours of the evolving functions form a new grid at each time. The velocity vector in the evolution equation is chosen according to the Geometric Conservation Law (GCL) method (Cao et al., SIAM J Sci Comput 24 (2002), 118,142.). This method has precise control over the Jacobian of transformation because of using the GCL method. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 [source] Projected Gradient Flows for BV/Level Set RelaxationPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2005Martin Burger This paper introduces a new level set method based on projected gradient flows for problems that can be solved by a recently introduced relaxation approach. For the class of problems the relaxation is exact, it can be shown that the solution of the flow converges to a solution of the relaxed problem for large time, and the level sets of the limit are solutions of the original problem. We introduce a simple computational scheme based on explicit time discretization and apply the method to imaging examples. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Direct simulation of the buoyant rise of bubbles in infinite liquid using level set methodTHE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 3 2008Zhao Yu Abstract In this study, 3-D level set method is applied to investigate the rise of gas bubbles in infinite liquid domain due to the buoyancy force. A number of typical regimes for single bubble rising are studied, including the ellipsoidal, ellipsoidal cap, spherical cap, and skirted bubbles. The bubble shape and rise velocity predicted by the simulation are compared with the graphical correlations of Grace, Trans. Inst. Chem. Eng., 51, 116,120, (1973) and Bhaga and Weber, J. Fluid Mech., 105, 61,85, (1981). Good agreement is found between the simulation results and the correlations. These simulations cover a wide range of the parameters, including Eo, Mo, and Re, and demonstrate the capability and accuracy of level set method for simulation of bubbles under various conditions with considerable deformation. Finally, simulation results for the coalescence of two bubbles are also presented. Dans cette étude, une méthode de level set en 3-D est utilisée pour examiner la montée des bulles de gaz due à la force de flottabilité dans un domaine liquide infini. Plusieurs régimes typiques de montée d'une bulle sont étudiés, dont le régime ellipsoïdal, le chapeau ellipsoïdal, le chapeau sphérique et les ceintures de bulles. La forme des bulles et la vitesse de montée prédites par la simulation sont comparées aux corrélations graphiques de Grace, Trans. Inst. Chem. Eng., 51, 116,120, (1973), et Bhaga et Weber, J. Fluid Mech., 105, 61,85, (1981). Un bon accord est trouvé entre les résultats des simulations et les corrélations. Ces simulations couvrent un large éventail de paramètres, notamment Eo, Mo, et Re, et montrent la capacité et la précision de la méthode level set pour la simulation des bulles dans des conditions diverses avec une déformation considérable. Enfin, les résultats des simulations sont également présentés pour la coalescence de deux bulles. [source] | ||||||||||