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We develop a decoupled, first-order, fully discrete, energy-stable scheme for the Cahn-Hilliard-Navier-Stokes equations. This scheme calculates the Cahn-Hilliard and Navier-Stokes equations separately, thus effectively decoupling the entire…

Numerical Analysis · Mathematics 2025-06-25 Haijun Gao , Xi Li , Minfu Feng

This article is concerned with the problem of determining an unknown source of non-potential, external time-dependent perturbations of an incompressible fluid from large-scale observations on the flow field. A relaxation-based approach is…

Analysis of PDEs · Mathematics 2024-02-26 Vincent R. Martinez

The paper presents numerical methods for unsteady flows of a viscous incompressible fluid in internal domains with many inlet/outlet sections. The novel variants of dissipative boundary conditions augmented by the inertia terms are used at…

Computational Physics · Physics 2019-12-10 Jacek Szumbarski

We present a novel framework inspired by the Immersed Boundary Method for predicting the fluid-structure interaction of complex structures immersed in flows with moderate to high Reynolds numbers. The main novelties of the proposed…

We develop a new numerical technique for approximating solutions of the Navier-Stokes equations on moving domains. The method aims at simulating an incompressible fluid past an object whose motion is assigned a priori using a level-set…

Numerical Analysis · Mathematics 2026-03-23 Hridya Dilip , Clarissa Astuto , Armando Coco , Giovanni Russo

We present a novel second-order semi-implicit hybrid finite volume / finite element (FV/FE) scheme for the numerical solution of the incompressible and weakly compressible Navier-Stokes equations on moving unstructured meshes using an…

Numerical Analysis · Mathematics 2023-01-24 Saray Busto , Michael Dumbser , Laura Río-Martín

We present a novel numerical method to solve the incompressible Navier-Stokes equations for two-phase flows with phase change, using a one-fluid approach. Separate phases are tracked using a geometric Volume-Of-Fluid (VOF) method with…

Computational Physics · Physics 2021-02-03 L. C. Malan , A. G. Malan , S. Zaleski , P. G. Rousseau

In this paper we present an efficient discretization method for the solution of the unsteady incompressible Navier-Stokes equations based on a high order (Hybrid) Discontinuous Galerkin formulation. The crucial component for the efficiency…

Numerical Analysis · Mathematics 2016-06-29 Christoph Lehrenfeld , Joachim Schöberl

A new time discretization scheme for the numerical simulation of two-phase flow governed by a thermodynamically consistent diffuse interface model is presented. The scheme is consistent in the sense that it allows for a discrete in time…

Analysis of PDEs · Mathematics 2014-02-27 Harald Garcke , Michael Hinze , Christian Kahle

Obtaining reliable numerical simulations of turbulent fluids is a challenging problem in computational fluid mechanics. The Large Eddy Simulations (LES) models are efficient tools to approximate turbulent fluids and an important step in the…

Analysis of PDEs · Mathematics 2018-05-23 Luigi C. Berselli , Stefano Spirito

In this paper, we derive first-order Euler finite element discretization schemes for a time-dependent natural convection model with variable density (NCVD). The model is governed by the variable density Navier-Stokes equations coupled with…

Numerical Analysis · Mathematics 2025-05-20 Li Hang , Chenyang Li

We provide a integration of Navier-Stokes equations concerning the unsteady-state laminar flow of an incompressible, isothermal (newtonian) fluid in a cylindrical vessel spinning about its symmetry axis, say $z$, and inside which the liquid…

Fluid Dynamics · Physics 2016-12-14 Alessio Bocci , Giovanni Mingari Scarpello , Daniele Ritelli

We present and analyze a fully discrete fractional time stepping technique for the solution of the micropolar Navier Stokes equations, which is a system of equations that describes the evolution of an incompressible fluid whose material…

Numerical Analysis · Mathematics 2013-12-06 Abner J. Salgado

The aim of this paper is to show time-decay estimates of solutions to linearized two-phase Navier-Stokes equations with surface tension and gravity. The original two-phase Navier-Stokes equations describe the two-phase incompressible…

Analysis of PDEs · Mathematics 2021-03-02 Hirokazu Saito

This paper addresses the numerical solution of the two-dimensional Navier--Stokes (NS) equations with nonsmooth initial data in the $L^2$ space, which is the critical space for the two-dimensional NS equations to be well-posed. In this…

Numerical Analysis · Mathematics 2025-10-02 Buyang Li , Qiqi Rao , Hui Zhang , Zhi Zhou

Based on a recent novel formulation of parametric anisotropic curve shortening flow, we analyse a fully discrete numerical method of this geometric evolution equation. The method uses piecewise linear finite elements in space and a backward…

Numerical Analysis · Mathematics 2023-03-01 Klaus Deckelnick , Robert Nürnberg

We present a simple and efficient variational finite difference method for simulating time-dependent Stokes flow in the presence of irregular free surfaces and moving solid boundaries. The method uses an embedded boundary approach on…

Computational Physics · Physics 2011-05-25 Christopher Batty , Robert Bridson

An efficient and accurate finite-element algorithm is described for the numerical solution of the incompressible Navier-Stokes (INS) equations. The new algorithm that solves the INS equations in a velocity-pressure reformulation is based on…

Numerical Analysis · Mathematics 2020-02-19 Longfei Li

We present the first convergence proof for an iso-parametric finite element discretization of two-phase Stokes flow in $\Omega \subset \mathbb{R}^d$, $d=2,3$, with interface dynamics governed by mean curvature. The proof relies on a crucial…

Numerical Analysis · Mathematics 2025-09-25 Genming Bai , Harald Garcke , Shravan Veerapaneni

A Cahn-Hilliard-Navier-Stokes system for two-phase flow on an evolving surface with non-matched densities is derived using methods from rational thermodynamics. For a Cahn-Hilliard energy with a singular (logarithmic) potential short time…

Analysis of PDEs · Mathematics 2025-11-18 Helmut Abels , Harald Garcke , Andrea Poiatti