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We propose a finite element discretization for the steady, generalized Navier-Stokes equations for fluids with shear-dependent viscosity, completed with inhomogeneous Dirichlet boundary conditions and an inhomogeneous divergence constraint.…

Numerical Analysis · Mathematics 2023-10-09 Julius Jeßberger , Alex Kaltenbach

High-order time-stepping schemes are crucial for simulating incompressible fluid flows due to their ability to capture complex turbulent behavior and unsteady motion. In this work, we propose a third-order accurate numerical scheme for the…

Numerical Analysis · Mathematics 2025-12-22 Kelong Cheng , Jingwei Sun , Hong Zhang

We prove that uniform accuracy of almost second order can be achieved with a finite difference method applied to Navier-Stokes flow at low Reynolds number with a moving boundary, or interface, creating jumps in the velocity gradient and…

Numerical Analysis · Mathematics 2016-07-27 J. Thomas Beale

We study the existence of weak martingale solutions to a stochastic moving boundary problem arising from the interaction between an isentropic compressible fluid and a viscoelastic structure. In the model, we consider a three-dimensional…

Analysis of PDEs · Mathematics 2025-05-22 Jeffrey Kuan , Krutika Tawri

Boundary integral methods are highly suited for problems with complicated geometries, but require special quadrature methods to accurately compute the singular and nearly singular layer potentials that appear in them. This paper presents a…

Numerical Analysis · Mathematics 2022-08-24 Joar Bagge , Anna-Karin Tornberg

We present a methodology for simulating three-dimensional flow of incompressible viscoplastic fluids modelled by generalised Newtonian rheological equations. It is implemented in a highly efficient framework for massively parallelisable…

Fluid Dynamics · Physics 2019-09-17 Knut Sverdrup , Ann Almgren , Nikolaos Nikiforakis

We propose and analyze computationally a new fictitious domain method, based on higher order space-time finite element discretizations, for the simulation of the nonstationary, incompressible Navier-Stokes equations on evolving domains. The…

Numerical Analysis · Mathematics 2022-06-22 Mathias Anselmann , Markus Bause

The lattice Boltzmann method has become a standard for efficiently solving problems in fluid dynamics. While unstructured grids allow for a more efficient geometrical representation of complex boundaries, the lattice Boltzmann methods is…

This work introduces a stabilised finite element formulation for the Stokes flow problem with a nonlinear slip boundary condition of friction type. The boundary condition is enforced with the help of an additional Lagrange multiplier and…

Numerical Analysis · Mathematics 2024-05-21 Tom Gustafsson , Juha Videman

We prove the existence of martingale solutions to a stochastic fluid-structure interaction problem involving a viscous, incompressible fluid flow, modeled by the Navier-Stokes equations, through a deformable elastic tube modeled by…

Analysis of PDEs · Mathematics 2024-02-22 Krutika Tawri

In this article, we analyse a stabilised equal-order finite element approximation for the Stokes equations on anisotropic meshes. In particular, we allow arbitrary anisotropies in a sub-domain, for example along the boundary of the domain,…

Numerical Analysis · Mathematics 2018-10-12 Stefan Frei

We study free boundary problems for incompressible inhomogeneous flows governed by the Navier--Stokes equations, focusing on the regularity and global-in-time well-posedness of solutions in critical functional frameworks for small initial…

Analysis of PDEs · Mathematics 2025-12-11 Piotr B. Mucha , Tomasz Piasecki , Yoshihiro Shibata

We introduce new control-volume finite-element discretization schemes suitable for solving the Stokes problem. Within a common framework, we present different approaches for constructing such schemes. The first and most established strategy…

Numerical Analysis · Mathematics 2025-02-05 Martin Schneider , Timo Koch

Simulating the interaction of fluids with immersed moving solids is playing an important role for gaining a better quantitative understanding of how fluid dynamics is altered by the presence of obstacles and which forces are exerted on the…

In this paper we propose a novel and general approach to design semi-implicit methods for the simulation of fluid-structure interaction problems in a fully Eulerian framework. In order to properly present the new method, we focus on the…

Numerical Analysis · Mathematics 2023-10-31 Mirco Ciallella , Thomas Milcent

In this paper, we propose a new virtual interpolation point method to formulate the discrete Stokes equations. We form virtual staggered structure for the velocity and pressure from the actual computation node set. The virtual interpolation…

Numerical Analysis · Mathematics 2014-01-28 Seong-Kwan Park , Gahyung Jo , Hi Jun Choe

We introduce an immersed high-order discontinuous Galerkin method for solving the compressible Navier-Stokes equations on non-boundary-fitted meshes. The flow equations are discretised with a mixed discontinuous Galerkin formulation and are…

Numerical Analysis · Mathematics 2020-01-08 Hong Xiao , Eky Febrianto , Qiaoling Zhang , Fehmi Cirak

Two-dimensional Stokes flow through a periodic channel is considered. The channel walls need only be Lipschitz continuous, in other words they are allowed to have corners. Boundary integral methods are an attractive tool for numerically…

Numerical Analysis · Mathematics 2020-05-11 Lukas Bystricky , Sara Pålsson , Anna-Karin Tornberg

We present a fluctuating boundary integral method (FBIM) for overdamped Brownian Dynamics (BD) of two-dimensional periodic suspensions of rigid particles of complex shape immersed in a Stokes fluid. We develop a novel approach for…

Numerical Analysis · Mathematics 2018-09-26 Yuanxun Bao , Manas Rachh , Eric Keaveny , Leslie Greengard , Aleksandar Donev

We study a colocated cell centered finite volume method for the approximation of the incompressible Navier-Stokes equations posed on a 2D or 3D finite domain. The discrete unknowns are the components of the velocity and the pressures, all…

Numerical Analysis · Mathematics 2008-04-30 Robert Eymard , Raphaele Herbin , Jean-Claude Latché