Related papers: Calculation of interface curvature with the level-…
The level-set method is a popular interface tracking method in two-phase flow simulations. An often-cited reason for using it is that the method naturally handles topological changes in the interface, e.g. merging drops, due to the implicit…
The present work illustrates a difficulty with the level-set method to accurately capture the curvature of interfaces in regions that are of equal distance to two or more interfaces. Such regions are characterized by kinks in the level-set…
We propose a deep learning strategy to estimate the mean curvature of two-dimensional implicit interfaces in the level-set method. Our approach is based on fitting feed-forward neural networks to synthetic data sets constructed from…
We present a novel hybrid strategy based on machine learning to improve curvature estimation in the level-set method. The proposed inference system couples enhanced neural networks with standard numerical schemes to compute curvature more…
In this paper we investigate the numerical approximation of a variant of the mean curvature flow. We consider the evolution of hypersurfaces with normal speed given by $H^k$, $k \ge 1$, where $H$ denotes the mean curvature. We use a level…
In numerical simulations of two-phase flows, the computation of the curvature of the interface is a crucial ingredient. Using a finite element and level set discretization, the discrete interface is typically the level set of a low order…
In this paper, a new re-initialization method for the conservative level-set function is put forward. First, it has been shown that the re-initialization and advection equations of the conservative level-set function are mathematically…
We extend thresholding methods for numerical realization of mean curvature flow on obstacles to the anisotropic setting where interfacial energy depends on the orientation of the interface. This type of schemes treats the interface…
In this paper we describe a high-resolution transport formulation of the regional level-set approach for an improved prediction of the evolution of complex interface networks. The novelty of this method is twofold: (i) construction of local…
In two-phase flow simulations, a difficult issue is usually the treatment of surface tension effects. These cause a pressure jump that is proportional to the curvature of the interface separating the two fluids. Since the evaluation of the…
Here a semi-implicit formulation of the gradient augmented level set method is presented. By tracking both the level set and it's gradient accurate subgrid information is provided,leading to highly accurate descriptions of a moving…
The dynamics of solid-liquid interfaces controlled by solute precipitation and/or dissolution due to the chemical reaction at the interface were computed in two dimensions using a phase field models. Sharp-interface asymptotic analysis…
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 propose a data-driven mean-curvature solver for the level-set method. This work is the natural extension to $\mathbb{R}^3$ of our two-dimensional strategy in [DOI: 10.1007/s10915-022-01952-2][1] and the hybrid inference system of [DOI:…
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 completely different approaches widely used in various applications. The…
A robust numerical methodology to predict equilibrium interfaces over arbitrary solid surfaces is developed. The kernel of the proposed method is the distance regularized level set equations (DRLSE) with techniques to incorporate the…
Many interfacial phenomena in physical and biological systems are dominated by high order geometric quantities such as curvature. Here a semi-implicit method is combined with a level set jet scheme to handle stiff nonlinear advection…
In this study, we investigate and compare formulations for computing shape derivatives in bi-material level-set optimization with precise modeling of the interface. The level-set function is parameterized using B-splines, whose coordinates…
This paper considers and proposes some algorithms to compute the mean curvature flow under topological changes. Instead of solving the fully nonlinear partial differential equations based on the level set approach, we propose some…
This paper is concerned with the study of a geometric flow whose law involves a singular integral operator. This operator is used to define a non-local mean curvature of a set. Moreover the associated flow appears in two important…