English
Related papers

Related papers: A Statistical Framework for Domain Shape Estimatio…

200 papers

This study investigates the asymptotic behavior of the steady-state quasi-Newtonian Stokesflow with viscosity given by the Carreau law within a thin domain, focusing on the effects of a slightly rough boundary of the domain. Employing…

Analysis of PDEs · Mathematics 2025-08-08 María Anguiano , Francisco J. Suárez-Grau

The dynamics of evolving fluid films in the viscous Stokes limit is relevant to various applications, such as the modeling of lipid bilayers in cells. While the governing equations were formulated by Scriven in 1960, solving for the flow of…

Fluid Dynamics · Physics 2025-01-29 Cuncheng Zhu , David Saintillan , Albert Chern

An alternative form of the general solution of the linearized stationary Navier-Stokes equations for an incompressible fluid in spherical coordinates is obtained by the vector potential method. A previously published solution to this…

Fluid Dynamics · Physics 2024-12-10 Peter Lebedev-Stepanov

A framework is developed for a robust and highly accurate numerical solution of the coupled Stokes-Darcy system in three dimensions. The domain decomposition method is based on a Dirichlet-Neumann type splitting of the interface conditions…

Numerical Analysis · Mathematics 2022-01-19 Svetlana Tlupova

We propose a procedure - partly analytical and partly numerical - to find the frequency and the damping rate of the small-amplitude oscillations of a massless elastic capsule immersed in a two-dimensional viscous incompressible fluid. The…

Fluid Dynamics · Physics 2014-04-03 Marco Martins Afonso , Simon Mendez , Franck Nicoud

Problems of particle dynamics involving unsteady Stokes flows in confined geometries are typically harder to solve than their steady counterparts. Approximation techniques are often the only resort. Felderhof (see e.g. 2005, 2009b) has…

Fluid Dynamics · Physics 2018-04-04 Akarsh Simha , Jianyong Mo , Philip J. Morrison

We consider a multi-dimensional model of a compressible fluid in a bounded domain. We want to estimate the density and velocity of the fluid, based on the observations for only velocity. We build an observer exploiting the symmetries of the…

Optimization and Control · Mathematics 2016-11-24 Amit Apte , Didier Auroux , Mythily Ramaswamy

We present a fast, high-order accurate and adaptive boundary integral scheme for solving the Stokes equations in complex---possibly nonsmooth---geometries in two dimensions. The key ingredient is a set of panel quadrature rules capable of…

Numerical Analysis · Mathematics 2020-04-22 Bowei Wu , Hai Zhu , Alex Barnett , Shravan Veerapaneni

Accurate simulations of ice sheet dynamics, mantle convection, lava flow, and other highly viscous free-surface flows involve solving the coupled Stokes/free-surface equations. In this paper, we theoretically analyze the stability and…

Numerical Analysis · Mathematics 2025-06-13 Igor Tominec , Lukas Lundgren , André Löfgren , Josefin Ahlkrona

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

We study the motion of a 1-D closed elastic string with bending and stretching energy immersed in a 2-D Stokes flow. In this paper we introduce the curve's tangent angle function and the stretching function to describe the deferent…

Analysis of PDEs · Mathematics 2020-11-12 Hui Li

Using limited observations of the velocity field of the two-dimensional Navier-Stokes equations, we successfully reconstruct the steady body force that drives the flow. The number of observed data points is less than 10\% of the number of…

Fluid Dynamics · Physics 2024-02-26 Aseel Farhat , Adam Larios , Vincent R. Martinez , Jared P. Whitehead

A stabilized finite element method is introduced for the simulation of time-periodic creeping flows, such as those found in the cardiorespiratory systems. The new technique, which is formulated in the frequency rather than time domain,…

Numerical Analysis · Mathematics 2022-11-30 Mahdi Esmaily

The existence and dynamical role of particular unstable Navier-Stokes solutions (exact coherent structures) is revealed in laboratory studies of weak turbulence in a thin, electromagnetically-driven fluid layer. We find that the dynamics…

Chaotic Dynamics · Physics 2018-08-01 Balachandra Suri , Jeffrey Tithof , Roman O. Grigoriev , Michael F. Schatz

We show that an attempt to compute numerically a viscous flow in a domain with a piece-wise smooth boundary by straightforwardly applying well-tested numerical algorithms (and numerical codes based on their use, such as COMSOL Multiphysics)…

Fluid Dynamics · Physics 2009-04-06 J. E. Sprittles , Y. D. Shikhmurzaev

We consider the quasistationary Stokes flow that describes the motion of a two-dimensional fluid body under the influence of surface tension effects in an unbounded, infinite-bottom geometry. We reformulate the problem as a fully nonlinear…

Analysis of PDEs · Mathematics 2024-04-25 Georg Prokert , Bogdan-Vasile Matioc

This paper is concerned with a numerical simulation of shape optimization in a two-dimensional viscous incompressible flow governed by Navier--Stokes equations with mixed boundary conditions containing the pressure. The minimization problem…

Optimization and Control · Mathematics 2007-05-23 Zhiming Gao , Yichen Ma

In this work we are interested in estimating the size of a cavity D immersed in a bounded domain \Omega, contained in R^d, d=2,3, filled with a viscous fluid governed by the Stokes system, by means of velocity and Cauchy forces on the…

Analysis of PDEs · Mathematics 2017-02-01 E. Beretta , C. Cavaterra , J. H. Ortega , S. Zamorano

The immersed boundary method is a numerical and mathematical formulation for solving fluid-structure interaction problems. It relies on solving fluid equations on an Eulerian fluid grid and interpolating the resulting velocity back onto…

Numerical Analysis · Mathematics 2020-03-19 Ondrej Maxian , Charles S. Peskin

We address the numerical solution of infinite-dimensional inverse problems in the framework of Bayesian inference. In the Part I companion to this paper (arXiv.org:1308.1313), we considered the linearized infinite-dimensional inverse…

Methodology · Statistics 2014-04-14 Noemi Petra , James Martin , Georg Stadler , Omar Ghattas