Related papers: A Novel Reinitialization Scheme for Conservative L…
We propose a level set method to reconstruct unknown surfaces from point clouds, without assuming that the connections between points are known. We consider a variational formulation with a curvature constraint that minimizes the surface…
Recently, machine learning has been used to substitute parts of conventional computational fluid dynamics, e.g. the cell-face reconstruction in finite-volume solvers or the curvature computation in the Volume-of-Fluid (VOF) method. The…
We focus on a geometrical inverse problem that involves recovering discontinuities in electrical conductivity based on boundary measurements. This problem serves as a model to introduce a shape recovery technique that merges the…
Aiming for the simulation of colloidal droplets in microfluidic devices, we present here a numerical method for two-fluid systems subject to surface tension and depletion forces among the suspended droplets. The algorithm is based on an…
Accurate representation of interfaces and flux exchange is vital for coupled multiphysics simulations across a broad range of applications. Currently, coupling approaches are limited by the underlying discretization or to specific physical…
In this paper, we introduce a novel way to represent the interface for two-phase flows with phase change. We combine a level-set method with a Cartesian embedded boundary method and take advantage of both. This is part of an effort to…
We propose a level-set-based semi-Lagrangian method on graded adaptive Cartesian grids to address the problem of surface reconstruction from point clouds. The goal is to obtain an implicit, high-quality representation of real shapes that…
The computation of multiphase flows presents a subtle energetic equilibrium between potential (i.e., surface) and kinetic energies. The use of traditional interface-capturing schemes provides no control over such a dynamic balance. In the…
When extended to two-phase flows, weakly compressible models lead to a non-conservative system, which precludes its treatment using standard finite volume techniques. In this paper, a novel HLLC-type path-conservative scheme is formulated…
Recent efforts to accelerate first-order methods have focused on convex optimization problems that satisfy a geometric property known as error-bound condition, which covers a broad class of problems, including piece-wise linear programs and…
Including derivative information in the modelling of moving interfaces has been proposed as one method to increase the accuracy of numerical schemes with minimal additional cost. Here a new level set reinitialization technique using the…
It is well-known that the standard level set advection equation does not preserve the signed distance property, which is a desirable property for the level set function representing a moving interface. Therefore, reinitialization or…
We have developed a new embedding method for solving scalar hyperbolic conservation laws on surfaces. The approach represents the interface implicitly by a signed distance function following the typical level set method and some embedding…
We present a novel interface-capturing scheme, THINC-scaling, to unify the VOF (volume of fluid) and the level set methods, which have been developed as two different approaches widely used in various applications. The key to success is to…
We introduce and analyze a lower envelope method (LEM) for the tracking of interfaces motion in multiphase problems. The main idea of the method is to define the phases as the regions where the lower envelope of a set of functions coincides…
Variational level set method has become a powerful tool in image segmentation due to its ability to handle complex topological changes and maintain continuity and smoothness in the process of evolution. However its evolution process can be…
A novel finite element framework is proposed for the numerical simulation of two phase flows with surface tension. The Level-Set (LS) method with piece-wise quadratic (P2) interpolation for the liquid-gas interface is used in order to reach…
This paper proposes a level set-based method for optimizing shell structures with large design changes in shape and topology. Conventional shell optimization methods, whether parametric or nonparametric, often only allow limited design…
The accuracy of finite element solutions is closely tied to the mesh quality. In particular, geometrically nonlinear problems involving large and strongly localized deformations often result in prohibitively large element distortions. In…
This paper presents a new parameter free partially penalized immersed finite element method and convergence analysis for solving second order elliptic interface problems. A lifting operator is introduced on interface edges to ensure the…