A review of level-set methods and some recent applications

F Gibou, R Fedkiw, S Osher - Journal of Computational Physics, 2018 - Elsevier
We review some of the recent advances in level-set methods and their applications. In
particular, we discuss how to impose boundary conditions at irregular domains and free …

INN: Interfaced neural networks as an accessible meshless approach for solving interface PDE problems

S Wu, B Lu - Journal of Computational Physics, 2022 - Elsevier
Abstract Machine learning has been successfully applied to various fields in computational
science and engineering. In this paper, we propose interfaced neural networks (INNs) to …

Sharp interface approaches and deep learning techniques for multiphase flows

F Gibou, D Hyde, R Fedkiw - Journal of Computational Physics, 2019 - Elsevier
We present a review on numerical methods for simulating multiphase and free surface flows.
We focus in particular on numerical methods that seek to preserve the discontinuous nature …

An extension to Voro++ for multithreaded computation of Voronoi cells

J Lu, EA Lazar, CH Rycroft - Computer Physics Communications, 2023 - Elsevier
Voro++ is a software library written in C++ for computing the Voronoi tessellation, a
technique in computational geometry that is widely used for analyzing systems of particles …

Power diagrams and sparse paged grids for high resolution adaptive liquids

M Aanjaneya, M Gao, H Liu, C Batty… - ACM Transactions on …, 2017 - dl.acm.org
We present an efficient and scalable octree-inspired fluid simulation framework with the
flexibility to leverage adaptivity in any part of the computational domain, even when …

A mesh-free method using piecewise deep neural network for elliptic interface problems

C He, X Hu, L Mu - Journal of Computational and Applied Mathematics, 2022 - Elsevier
In this paper, we propose a novel mesh-free numerical method for solving the elliptic
interface problems based on deep learning. We approximate the solution by the neural …

Optimal local truncation error method for solution of 3-D Poisson equation with irregular interfaces and unfitted Cartesian meshes as well as for post-processing

A Idesman, M Mobin - Advances in Engineering Software, 2022 - Elsevier
Recently the optimal local truncation error method (OLTEM) has been developed for the 2-D
Poisson equation for heterogeneous materials with irregular interfaces and unfitted …

Second order finite-difference ghost-point multigrid methods for elliptic problems with discontinuous coefficients on an arbitrary interface

A Coco, G Russo - Journal of Computational Physics, 2018 - Elsevier
In this paper we propose a second-order accurate numerical method to solve elliptic
problems with discontinuous coefficients (with general non-homogeneous jumps in the …

An efficient meshfree method based on Pascal polynomials and multiple-scale approach for numerical solution of 2-D and 3-D second order elliptic interface problems

Ö Oruç - Journal of Computational Physics, 2021 - Elsevier
In this work, we propose an efficient meshfree method based on Pascal polynomials and
multiple-scale approach for numerical solutions of two-dimensional (2-D) and three …

On two-phase flow solvers in irregular domains with contact line

M Lepilliez, ER Popescu, F Gibou, S Tanguy - Journal of Computational …, 2016 - Elsevier
We present numerical methods that enable the direct numerical simulation of two-phase
flows in irregular domains. A method is presented to account for surface tension effects in a …