Related papers: A Paraboloid Fitting Technique for Calculating Cur…

We present a particle method for estimating the curvature of interfaces in volume-of-fluid simulations of multiphase flows. The method is well suited for under-resolved interfaces, and it is shown to be more accurate than the parabolic…

In spite of considerable progress, computing curvature in Volume of Fluid (VOF) methods continues to be a challenge. The goal is to develop a function or a subroutine that returns the curvature in computational cells containing an interface…

This paper evaluates and compares the accuracy and robustness of curvature estimation methods for three-dimensional interfaces represented implicitly by discrete volume fractions on a Cartesian mesh. The height function (HF) method is…

For capillary driven flow the interface curvature is essential in the modelling of surface tension via the imposition of the Young--Laplace jump condition. We show that traditional geometric volume of fluid (VOF) methods, that are based on…

Unstructured meshes are among the most versatile approaches for capturing non-canonical geometries in fluid dynamics simulations. Despite this, most high-fidelity first-principles phase-change models are developed and applied on structured…

This paper introduces a novel method for the efficient and accurate computation of volume fractions on unstructured polyhedral meshes, where the phase boundary is an orientable hypersurface, implicitly given as the iso-contour of a…

Utilizing recently developed abstract notions of sectional curvature, we introduce a method for constructing a curvature-based geometric profile of discrete metric spaces. The curvature concept that we use here captures the metric relations…

We present a three-dimensional (3D) common-refinement method for non-matching meshes between discrete non-overlapping subdomains of incompressible fluid and nonlinear hyperelastic structure. To begin, we first investigate the accuracy of…

Available algorithms for the initialization of volume fractions typically utilize exact functions to model fluid interfaces, or they rely on computationally costly intersections between volume meshes. Here, a new algorithm is proposed that…

The existing combinatorial methods for iso-surface computation are efficient for pure visualization purposes, but it is known that the resulting iso-surfaces can have holes, and topological problems like missing or wrong connectivity can…

We present a novel algorithm to compute multi-scale curvature fields on triangle meshes. Our algorithm is based on finding robust mean curvatures using the ball neighborhood, where the radius of a ball corresponds to the scale of the…

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…

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…

The flow within adhering droplets subjected to external shear flows has a significant influence on the stability and eventual detachment of the droplets from the surface. Most commonly, the velocity field inside adhering droplets is…

Simulations involving free surfaces and fluid interfaces are important in many areas of engineering. There is, however, still a need for improved simulation methods. Recently, a new efficient geometric VOF method called isoAdvector for…

Computational mathematics plays an increasingly important role in computational fluid dynamics (CFD). The aeronautics and aerospace re- search community is working on next generation of CFD capacity that is accurate, automatic, and fast. A…

The accurate reconstruction of immiscible fluid-fluid interfaces from the volume fraction field is a critical component of geometric Volume of Fluid (VOF) methods. A common strategy is the Piecewise Linear Interface Calculation (PLIC),…

We investigate discrete spin transformations, a geometric framework to manipulate surface meshes by controlling mean curvature. Applications include surface fairing -- flowing a mesh onto say, a reference sphere -- and mesh extrusion --…

Due to the computationally demanding nature of fluid-structure interaction simulations, heart valve simulation is a complex task. A simpler alternative is to model the valve as a resistive flow obstacle that can be updated dynamically…

Discrete forms of the mean and directed curvature are constructed on piecewise flat manifolds, providing local curvature approximations for smooth manifolds embedded in both Euclidean and non-Euclidean spaces. The resulting expressions take…