Results 1  10
of
63
A Hybrid Particle Level Set Method for Improved Interface Capturing
 J. Comput. Phys
, 2002
"... In this paper, we propose a new numerical method for improving the mass conservation properties of the level set method when the interface is passively advected in a flow field. Our method uses Lagrangian marker particles to rebuild the level set in regions which are underresolved. This is ofte ..."
Abstract

Cited by 219 (25 self)
 Add to MetaCart
(Show Context)
In this paper, we propose a new numerical method for improving the mass conservation properties of the level set method when the interface is passively advected in a flow field. Our method uses Lagrangian marker particles to rebuild the level set in regions which are underresolved. This is often the case for flows undergoing stretching and tearing. The overall method maintains a smooth geometrical description of the interface and the implementation simplicity characteristic of the level set method. Our method compares favorably with volume of fluid methods in the conservation of mass and purely Lagrangian schemes for interface resolution. The method is presented in three spatial dimensions.
An Eulerian formulation for solving partial differential equations along a moving interface
 Jardin Botanique  BP 101  54602 VillerslsNancy Cedex (France) Unit de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu  35042 Rennes Cedex (France) Unit de recherche INRIA RhneAlpes : 655, avenue de l'Europe  38334 Montbonnot Saint
, 2002
"... ..."
(Show Context)
Transport and diffusion of material quantities on propagating interfaces via level set methods
 Journal of Computational Physics
, 2003
"... We develop theory and numerical algorithms to apply level set methods to problems involving the transport and diffusion of material quantities in a level set framework. Level set methods are computational techniques for tracking moving interfaces; they work by embedding the propagating interface as ..."
Abstract

Cited by 39 (4 self)
 Add to MetaCart
(Show Context)
We develop theory and numerical algorithms to apply level set methods to problems involving the transport and diffusion of material quantities in a level set framework. Level set methods are computational techniques for tracking moving interfaces; they work by embedding the propagating interface as the zero level set of a higher dimensional function, and then approximate the solution of the resulting initial value partial differential equation using upwind finite difference schemes. The traditional level set method works in the trace space of the evolving interface, and hence disregards any parameterization in the interface description. Consequently, material quantities on the interface which themselves are transported under the interface motion are not easily handled in this framework. We develop model equations and algorithmic techniques to extend the level set method to include these problems. We demonstrate the accuracy of our approach through a series of test examples and convergence studies. 1
Structured Extended Finite Element Methods for Solids Defined By Implicit Surfaces
, 2003
"... this paper we describe a methodology for constructing the #nite elements for structured meshes for objects described by implicit surfaces, both for the outside boundary and interior surfaces. For existing parts, a laser scan of body can be immediately translated into an implicit description of the e ..."
Abstract

Cited by 12 (1 self)
 Add to MetaCart
this paper we describe a methodology for constructing the #nite elements for structured meshes for objects described by implicit surfaces, both for the outside boundary and interior surfaces. For existing parts, a laser scan of body can be immediately translated into an implicit description of the external boundaries. By means of holography and other methods, implicit function descriptions of any internal surfaces can also be obtained. They can then be translated to #nite element models as described here. For CAD models or solid models, the construction of an implicit surface model is also straightforward, for it is only necessary to extract a set of surface points from the geometric model. Thus, the paradigm described here should enable #nite element analyses of complex engineering problems with almost no human intervention. The concept of describing internal surfaces of a problem independent of a mesh by implicit functions originated in Sukumar et al. [10]. It has been used to model crack growth with level sets in two dimensions by Stolarska et al. [11], crack growth in three dimensions by Gravouil et al. [12]. The methodology has also been applied to solidi#cation, Chessa et al. [13] and #uid interfaces, Chessa et al. [14], and for particles in #uids by Wagner et al. [15]
Advecting normal vectors: a new method for calculating interface normals and curvatures when modeling twophase flows
 J. Comput. Phys
"... In simulating twophase flows, interface normal vectors and curvatures are needed for modeling surface tension. In the traditional approach, these quantities are calculated from the spatial derivatives of a scalar function (e.g. the volumeoffluid or the level set function) at any instant in time. ..."
Abstract

Cited by 11 (2 self)
 Add to MetaCart
(Show Context)
In simulating twophase flows, interface normal vectors and curvatures are needed for modeling surface tension. In the traditional approach, these quantities are calculated from the spatial derivatives of a scalar function (e.g. the volumeoffluid or the level set function) at any instant in time. The orders of accuracy of normals and curvatures calculated from these functions are studied. A new method for calculating these quantities is then presented, where the interface unit normals are advected along with whatever function represents the interface, and curvatures are calculated directly from these advected normals. To illustrate this new approach, the volumeoffluid method is used to represent the interface, and the advected normals are used for interface reconstruction. The accuracy and performance of the new method are demonstrated via test cases with prescribed velocity fields. The results are compared with those of traditional approaches.
SelfRepelling Snakes for TopologyPreserving Segmentation Models
"... Abstract—The implicit framework of the levelset method has several advantages when tracking propagating fronts. Indeed, the evolving contour is embedded in a higher dimensional levelset function and its evolution can be phrased in terms of a Eulerian formulation. The ability of this intrinsic meth ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
Abstract—The implicit framework of the levelset method has several advantages when tracking propagating fronts. Indeed, the evolving contour is embedded in a higher dimensional levelset function and its evolution can be phrased in terms of a Eulerian formulation. The ability of this intrinsic method to handle topological changes (merging and breaking) makes it useful in a wide range of applications (fluid mechanics, computer vision) and particularly in image segmentation, the main subject of this paper. Nevertheless, in some applications, this topological flexibility turns out to be undesirable: for instance, when the shape to be detected has a known topology, or when the resulting shape must be homeomorphic to the initial one. The necessity of designing topologypreserving processes arises in medical imaging, for example, in the human cortex reconstruction. It is known that the human cortex has a spherical topology so throughout the reconstruction process this topological feature must be preserved. Therefore, we propose in this paper a segmentation model based on an implicit levelset formulation and on the geodesic active contours, in which a topological constraint is enforced. Index Terms—Additive operator splitting (AOS) scheme, geodesic active contours, levelset method, segmentation, topology preservation. I.
A simple second order cartesian scheme for compressible Euler flows
, 2012
"... We present a finitevolume scheme for compressible Euler flows where the grid is cartesian and it does not fit to the body. The scheme, based on the definition of an ad hoc Riemann problem at solid boundaries, is simple to implement and it is formally second order accurate. Error convergence rates w ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
(Show Context)
We present a finitevolume scheme for compressible Euler flows where the grid is cartesian and it does not fit to the body. The scheme, based on the definition of an ad hoc Riemann problem at solid boundaries, is simple to implement and it is formally second order accurate. Error convergence rates with respect to several exact test cases are investigated and examples of flow solutions in one, two and three dimensions are presented. 1
A Corner Tracker Snake Approach to Segment Irregular Object Shapein Video Image
 IEEE International Conference on Acoustics, Speech and Signal Processing, Las Vegas: United States
, 2008
"... A corner tracker snake approach to segment irregular object shape in video image, Proceedings of the IEEE ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
(Show Context)
A corner tracker snake approach to segment irregular object shape in video image, Proceedings of the IEEE
A hybrid LagrangianEulerian approach for twophase flows with fully resolved interfaces
 ILASS America’s 20th Annual Conference on Liquid Atomization and Spray Systems
, 2007
"... A mutiscale numerical approach is developed for the investigation of bubbly flows in turbulent environments. This consists of two different numerical approaches capable of capturing the bubble dynamics at different scales depending upon the relative size of the bubbles compared to the grid resolu ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
(Show Context)
A mutiscale numerical approach is developed for the investigation of bubbly flows in turbulent environments. This consists of two different numerical approaches capable of capturing the bubble dynamics at different scales depending upon the relative size of the bubbles compared to the grid resolution: (i) fully resolved simulations (FRS) wherein the bubble dynamics and deformation are completely resolved, and (ii) subgrid, discrete bubble model where the bubbles are not resolved by the computational grid. For fully resolved simulations, a novel approach combining a particlebased, meshfree technique with a finitevolume flow solver, is developed. The approach uses marker points around the interface and advects the signed distance to the interface in a Lagrangian frame. Interpolation kernel based derivative calculations typical of particle methods are used to extract the interface normal and curvature from unordered marker points. Unlike fronttracking methods, connectivity between the marker points is not necessary. For underresolved bubbles, a mixturetheory based EulerianLagrangian approach accounting for volumetric displacements due to bubble motion and size variations is developed. The bubble dynamics is modeled by RayleighPlesset equations using an adaptive timestepping scheme. A detailed verification and validation study of both approaches is performed to test the accuracy of the method on a variety of single and multiple bubble problems to show good predictive capability. Interaction of bubbles with a traveling vortex tube is simulated and compared with experimental data of ∗Address all correspondence to this author. Sridhar and Katz [1] to show good agreement. 1