Related papers: Application of the level-set method to the implici…
The level set approach represents surfaces implicitly, and advects them by evolving a level set function, which is numerically defined on an Eulerian grid. Here we present an approach that augments the level set function values by gradient…
We present an approach for computing extensions of velocities or other fields in level set methods by solving a biharmonic equation. The approach differs from other commonly used approaches to velocity extension because it deals with the…
We present an adaptive reduced-order model for the efficient time-resolved simulation of fluid-structure interaction problems with complex and non-linear deformations. The model is based on repeated linearizations of the structural balance…
In this paper, a methodology for modelling two-phase flows based on a conservative level set method in the framework of finite volume method is presented. The novelty of the interface capturing method used here lies on the advection of…
Reduced-order models based on level-set methods are widely used tools to qualitatively capture and track the nonlinear dynamics of an interface. The aim of this paper is to develop a physics-informed, data-driven, statistically rigorous…
A passively advected sharp interface can be represented as the zero level set of a level set function $f$. The linear transport equation $\partial_tf+v\cdot \nabla f =0$ is the simplest governing equation for such a level set function.…
Surface-tension-dominant droplet evaporation is ubiquitous and of importance to many applications. We present an improved Coupled Level Set and Volume of Fluid (i-CLSVoF) framework without explicit interface reconstruction for modelling…
Existing 3D surface representation approaches are unable to accurately classify pixels and their orientation lying on the boundary of an object. Thus resulting in coarse representations which usually require post-processing steps to extract…
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…
In this paper, a parametric level set method for reconstruction of obstacles in general inverse problems is considered. General evolution equations for the reconstruction of unknown obstacles are derived in terms of the underlying level set…
The paper studies a method for solving elliptic partial differential equations posed on hypersurfaces in $\mathbb{R}^N$, $N=2,3$. The method allows a surface to be given implicitly as a zero level of a level set function. A surface equation…
A variational theory is developed to study electrolyte solutions, composed of interacting point-like ions in a solvent, in the presence of dielectric discontinuities and charges at the boundaries. Three important and non-linear…
3D shape analysis has been largely focused on traditional 3D representations of point clouds and meshes, but the discrete nature of these data makes the analysis susceptible to variations in input resolutions. Recent development of neural…
In this paper we study a system of advection-diffusion equations in a bulk domain coupled to an advection-diffusion equation on an embedded surface. Such systems of coupled partial differential equations arise in, for example, the modeling…
We present the theory and implementation of a Poisson-Boltzmann implicit solvation model for electrolyte solutions. This model can be combined with arbitrary electronic structure methods that provide an accurate charge density of the…
We introduce a novel concept, the minimal molecular surface (MMS), as a new paradigm for the theoretical modeling of biomolecule-solvent interfaces. When a less polar macromolecule is immersed in a polar environment, the surface free energy…
Accurate modeling of the solvent environment for biological molecules is crucial for computational biology and drug design. A popular approach to achieve long simulation time scales for large system sizes is to incorporate the effect of the…
The Immersed Interface Method is employed to solve the time-varying electric field equations around a three-dimensional vesicle. To achieve second-order accuracy the implicit jump conditions for the electric potential, up to the second…
An improved numerical solver for the unified solution of compressible and incompressible fluids involving interfaces is proposed. The present method is based on the CIP-CUP (Cubic Interpolated Propagation / Combined, Unified Procedure)…
A method of simulating the drying process of a soft matter solution with an implicit solvent model by moving the liquid-vapor interface is applied to various solution films and droplets. For a solution of a polymer and nanoparticles, we…