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We present an efficient and accurate immersed boundary (IB) finite element (FE) solver for numerically solving incompressible Navier--Stokes equations. Particular emphasis is given to internal flows with complex geometries (blood flow in…

Computational Engineering, Finance, and Science · Computer Science 2020-07-07 G. C. Bourantas , D. L. Lampropoulos , B. F. Zwick , V. C. Loukopoulos , A. Wittek , K. Miller

We present a comparison between the performance of solvers based on Nystr\"om discretizations of several well-posed boundary integral equation formulations of Helmholtz transmission problems in two-dimensional Lipschitz domains.…

Numerical Analysis · Mathematics 2016-05-13 Victor Dominguez , Mark Lyon , Catalin Turc

We present reduced basis approximations and rigorous a posteriori error bounds for the instationary Stokes equations. We shall discuss both a method based on the standard formulation as well as a method based on a penalty approach, which…

Numerical Analysis · Mathematics 2012-11-06 Anna-Lena Gerner , Arnold Reusken , Karen Veroy

We present a finite-difference scheme which solves the Stokes problem in the presence of curvilinear non-conforming interfaces and provides second-order accuracy on physical field (velocity, vorticity) and especially on pressure. The gist…

Fluid Dynamics · Physics 2011-10-07 Abdelkader Hammouti , Anaël Lemaître

This paper is concerned with the boundary integral equation method for solving the exterior Neumann boundary value problem of dynamic poroelasticity in two dimensions. The main contribution of this work consists of two aspescts: the…

Computational Physics · Physics 2020-08-18 Lu Zhang , Liwei Xu , Tao Yin

In this article, we derive \textit{a posteriori} error estimates for the Dirichlet boundary control problem governed by Stokes equation. An energy-based method has been deployed to solve the Dirichlet boundary control problem. We employ an…

Numerical Analysis · Mathematics 2024-01-30 Thirupathi Gudi , Ramesh Chandra Sau

In the present work, we propose to extend to the Stokes problem a fictitious domain approach inspired by eXtended Finite Element Method and studied for Poisson problem in [Renard]. The method allows computations in domains whose boundaries…

Numerical Analysis · Mathematics 2015-06-15 Sébastien Court , Michel Fournié , Alexei Lozinski

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

Stokes flow equations have been implemented successfully in practice for simulating problems with moving interfaces. Though computational methods produce accurate solutions and numerical convergence can be demonstrated using a resolution…

Numerical Analysis · Mathematics 2023-02-17 Haixia Dong , Zhongshu Zhao , Shuwang Li , Wenjun Ying , Jiwei Zhang

This paper proposes and analyzes a full discretization of the exterior transient Stokes problem with Dirichlet boundary conditions. The method is based on a single layer boundary integral representation, using Galerkin semidiscretization in…

Numerical Analysis · Mathematics 2014-10-14 Constantin Bacuta , Matthew E. Hassell , George C. Hsiao , Francisco-Javier Sayas

We investigate several robust preconditioners for solving the saddle-point linear systems that arise from spatial discretization of unsteady and steady variable-coefficient Stokes equations on a uniform staggered grid. Building on the…

Numerical Analysis · Mathematics 2016-08-24 M. Cai , A. J. Nonaka , J. B. Bell , B. E. Griffith , A. Donev

We present a numerical method for computing the single layer (Stokeslet) and double layer (stresslet) integrals in Stokes flow. The method applies to smooth, closed surfaces in three dimensions, and achieves high accuracy both on and near…

Numerical Analysis · Mathematics 2019-03-22 Svetlana Tlupova , J. Thomas Beale

This text proposes a fast, rapidly convergent Nystr\"{o}m method for the solution of the Lippmann-Schwinger integral equation that mathematically models the scattering of time-harmonic acoustic waves by inhomogeneous obstacles, while…

Numerical Analysis · Mathematics 2016-03-23 Akash Anand , Ambuj Pandey , B. V. Rathish Kumar , Jagabandhu Paul

This paper introduces a new immersed boundary (IB) method for viscous incompressible flow, based on a Fourier spectral method for the fluid solver and on the nonuniform fast Fourier transform (NUFFT) algorithm for coupling the fluid with…

Fluid Dynamics · Physics 2023-02-20 Zhe Chen , Charles S. Peskin

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 study flows generated within a two-dimensional corner by the chemical activity of the confining boundaries. Catalytic reactions at the surfaces induce diffusioosmotic motion of the viscous fluid throughout the domain. The presence of…

Fluid Dynamics · Physics 2026-01-21 Dobromir Nowak , Maciej Lisicki

We study periodic solutions to the Navier-Stokes equations. The transition phase of a dynamic Navier-Stokes solution to the periodic-in-time state can be excessively long and it depends on parameters like the domain size and the viscosity.…

Numerical Analysis · Mathematics 2019-12-30 Thomas Richter

Boundary integral methods are advantageous when simulating viscous flow around rigid particles, due to the reduction in number of unknowns and straightforward handling of the geometry. In this work we present a fast and accurate framework…

Numerical Analysis · Mathematics 2016-09-22 Ludvig af Klinteberg , Anna-Karin Tornberg

This paper provides a rigorous analysis of boundary element methods for the magnetic field integral equation on Lipschitz polyhedra. The magnetic field integral equation is widely used in practical applications to model electromagnetic…

Numerical Analysis · Mathematics 2024-09-12 Van Chien Le , Kristof Cools

We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in $\R^n$ with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-flat…

Analysis of PDEs · Mathematics 2009-01-05 Gui-Qiang Chen , Dan Osborne , Zhongmin Qian