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 under-resolved. 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.

In this paper, we present an e#cient semi-Lagrangian based particle level set method for the accurate capturing of interfaces. This method retains the robust topological properties of the level set method without the adverse e#ects of numerical dissipation. Both the level set method and the particle level set method typically use high order accurate numerical discretizations in time and space, e.g. TVD RungeKutta and HJ-WENO schemes. We demonstrate that these computationally expensive schemes are not required. Instead, fast, low order accurate numerical schemes su#ce. That is, the addition of particles to the level set method not only removes the di#culties associated with numerical di#usion, but also alleviates the need for computationally expensive high order accurate schemes. We use an e#cient, first order accurate semi-Lagrangian advection scheme coupled with a first order accurate fast marching method to evolve the level set function. To accurately track the underlying flow characteristics, the particles are evolved with a second order accurate method. Since we avoid complex high order accurate numerical methods, extending the algorithm to arbitrary data structures becomes more feasible, and we show preliminary results obtained with an octree-based adaptive mesh.

In this paper, we present a level set approach for the modeling of dendritic solidification. These simulations exploit a recently developed second order accurate symmetric discretization of the Poisson equation, see [12]. Numerical results indicate that this method can be used successfully on complex interfacial shapes and can simulate many of the physical features of dendritic solidification. We apply this algorithm to the simulation of the dendritic crystallization of a pure melt and find that the dendrite tip velocity and tip shapes are in excellent agreement with solvability theory. Numerical results are presented in both two and three spatial dimensions.

Abstract not found

Level set methods have gained popularity in a number of research areas from computational physics to computer vision to computer graphics. They provide for a robust representation of geometry that can be dynamically evolved by solving partial differential equations in a manner that has been fine tuned by a community of researchers over a number of years. Traditionally, simulation of natural phenomena has been the focus of the computational physics community, but more recently computer graphics researchers have become interested in these methods in part because water, smoke and fire are exciting elements in high demand for special effects in feature films.

this article we give a brief overview of the level set method, the use of the ghost fluid method for modeling discontinuities across the interface, the "particle level set method" for tracking contact discontinuities, and illustrate the use of these methods in the context of computer animation. Additional details concerning these methods can be found in the recently published book, "Level Set Methods and Dynamic Implicit Surfaces" [28]

The animation of volcanic smoke is useful for natural disaster simulations, entertainments, etc. In this paper, we propose a model to generate realistic animations of the volcanic smoke. The model is designed by taking the eruption magnitude decided by the eruption velocity and the initial volcanic smoke density, the buoyancy generated by the difference between the volcanic smoke density and the atmospheric density, and the decreasing of the volcanic smoke density due to the loss of the pyroclasts (fragments of magma); i.e., this model is based on the physical dynamics of the volcanic smoke. In this model, the Navier-Stokes equations are used, and we solve the equations by using the method of the Coupled Map Lattice (CML) that is an efficient solver. Hence, in our system, the behavior of the volcanic smoke can be calculated in practical calculation time, and various shapes of the volcanic smoke can be generated by only changing some parameters. Therefore, realistic volcanic smoke animations can be created by our approach efficiently. 1

Surface reconstruction from particle system is a difficult problem. In this paper, we introduce a method to reconstruct the surface from particle-based simulation of ocean waves with complex shape and splashes. Each 2D slice of particle volume is projected onto an image, and then the image is segmented for recognition of water body and splash fragments. Outlines of the water body are extracted directionally. The mesh of surface is reconstructed by tiling the triangular strip from the outlines of the slices. The experiments show that the efficiency of this method is very competitive. 1.

In this paper, we present an enhanced resolution capturing method for topologically complex two and three dimensional incompressible free surface flows. The method is based upon the level set method of Osher and Sethian to represent the interface combined with two recent advances in the treatment of the interface, a second order accurate discretization of the Dirichlet pressure boundary condition at the free surface (2002, J. Comput. Phys. 176, 205) and the use of massless marker particles to enhance the resolution of the interface through the use of the particle level set method (2002, J. Comput. Phys., 183, 83).