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We investigate the asymmetric freezing of a liquid droplet sliding on an inclined cold surface using numerical simulations based on the lubrication approximation. The combined effects of gravity, capillarity, and solidification kinetics on…

The developments over the last five decades concerning numerical discretisations of the incompressible Navier--Stokes equations have lead to reliable tools for their approximation: those include stable methods to properly address the…

Numerical Analysis · Mathematics 2025-08-12 Dominic Breit , Andreas Prohl , Jörn Wichmann

We show the existence of weak solutions to the fluid-structure interaction problem of a largely deforming viscoelastic bulk solid with a viscous fluid governed by the incompressible Navier-Stokes equations. In contrast to previous works,…

Analysis of PDEs · Mathematics 2026-03-13 Antonín Češík , Malte Kampschulte , Sebastian Schwarzacher

In the present work, we investigate a numerical one-dimensional solver to the Navier-Stokes equation that retains all terms, including both pressure and dissipation. Solutions to simple examples that illustrate the actions of the nonlinear…

Fluid Dynamics · Physics 2023-03-30 Preben Buchhave , Clara Marika Velte

We consider surface finite elements and a semi-implicit time stepping scheme to simulate fluid deformable surfaces. Such surfaces are modeled by incompressible surface Navier-Stokes equations with bending forces. Here, we consider closed…

Numerical Analysis · Mathematics 2023-05-03 Veit Krause , Axel Voigt

In this work, we ask and answer the question: when is the viscosity of a fluid uniquely determined from spatially sparse measurements of its velocity field? We pose the question mathematically as an optimization problem using the…

Analysis of PDEs · Mathematics 2023-02-23 Animikh Biswas , Joshua Hudson

The settling of highly elastic non-Brownian closed fibres (called loops) under gravity in a viscous fluid is investigated numerically. The loops are represented using a bead-spring model with harmonic bending potential and finitely…

Soft Condensed Matter · Physics 2025-06-18 Yevgen Melikhov , Maria L. Ekiel-Jezewska

Modelling the flow in a thin accretion disc like a dynamical system, we analyse the nature of the critical points of the steady solutions of the flow. For the simple inviscid disc there are two critical points, with the outer one being a…

Astrophysics · Physics 2007-05-23 Arnab K. Ray , J. K. Bhattacharjee

This paper represents a sequel to the previous one, where numerical solution of a quasistatic contact problem is considered for an elastic body in frictional contact with a moving foundation. The model takes into account wear of the contact…

Numerical Analysis · Mathematics 2019-05-15 Danfu Han , Weimin Han , Michal Jureczka , Anna Ochal

In this paper we propose a numerical method to solve a 2D advection-diffusion equation, in the highly oscillatory regime. We use an efficient and robust integrator which leads to an accurate approximation of the solution without any time…

Numerical Analysis · Mathematics 2023-07-27 Clarissa Astuto , Mohammed Lemou , Giovanni Russo

We consider the well-posedness and numerical approximation of a Hamilton--Jacobi equation on an evolving hypersurface in $\mathbb R^3$. Definitions of viscosity sub- and supersolutions are extended in a natural way to evolving hypersurfaces…

Numerical Analysis · Mathematics 2018-10-09 Klaus Deckelnick , Charles M. Elliott , Tatsu-Hiko Miura , Vanessa Styles

Exponential stabilizability of the incompressible Navier-Stokes equations under dynamic slip boundary conditions toward arbitrary time-dependent trajectories is proven. The feedback control law is constructed explicitly using oblique…

Analysis of PDEs · Mathematics 2026-02-12 Buddhika Priyasad , Sérgio S. Rodrigues

This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…

Statistical Mechanics · Physics 2011-09-09 Guy Fayolle , Cyril Furtlehner

We propose a mixed finite element method for the motion of a strongly viscous, ideal, and isentropic gas. At the boundary we impose a Navier-slip condition such that the velocity equation can be posed in mixed form with the vorticity as an…

Numerical Analysis · Mathematics 2009-11-11 Kenneth Karlsen , Trygve Karper

The paper considers a system of equations that models a lateral flow of a Boussinesq--Scriven fluid on a passively evolving surface embedded in $\mathbb{R}^3$. For the resulting Navier-Stokes type system, posed on a smooth closed…

Analysis of PDEs · Mathematics 2022-03-04 Maxim A. Olshanskii , Arnold Reusken , Alexander Zhiliakov

The viscosity of supercooled liquids notably increases with decreasing temperature, leading to solidification through a glass transition. This process is accompanied by dynamic heterogeneity, characterized by persistent dynamic spatial…

Soft Condensed Matter · Physics 2024-09-30 Kento Maeda , Atsushi Ikeda

The authors consider stochastic aspects of the stabilization problem for two and three-dimensional Oseen equations with help of feedback control defined on a part of the fluid boundary. Stochastic issues arise when inevitable unpredictable…

Analysis of PDEs · Mathematics 2007-05-23 Jinqiao Duan , Andrei V. Fursikov

The evolution of a localized vortex in stably stratified flow, within the Boussinesq approximation, is analyzed using the fluid impulse concept. The set of equations describing the temporal development of the fluid impulse has an…

Fluid Dynamics · Physics 2021-12-14 Vladimir Levinski

We consider a fluid-structure interaction problem involving a viscous, incompressible fluid flow, modeled by the 2D Navier-Stokes equations, through a thin deformable elastic tube, displacement of which is not known a priori. The…

Analysis of PDEs · Mathematics 2026-04-09 Krutika Tawri , Nash Ward

In (J. Comput. Phys., 417, 109577, 2020) we introduced a space-time embedded-hybridizable discontinuous Galerkin method for the solution of the incompressible Navier-Stokes equations on time-dependent domains of which the motion of the…

Numerical Analysis · Mathematics 2023-07-07 Tamas L. Horvath , S. Rhebergen