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We develop and analyse an adaptive fully mixed finite element method for stationary generalized bioconvective flows, where the Navier--Stokes equations with concentration-dependent viscosity are coupled with a conservation law for swimming…

Numerical Analysis · Mathematics 2026-01-14 Eligio Colmenares , Ricardo Ruiz-Baier , Dalidet Sanhueza

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 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

We introduce a residual-based stabilized formulation for incompressible Navier-Stokes flow that maintains discrete (and, for divergence-conforming methods, strong) mass conservation for inf-sup stable spaces with $H^1$-conforming pressure…

Numerical Analysis · Mathematics 2019-11-07 John A. Evans , David Kamensky , Yuri Bazilevs

Simulating nonlinear partial differential equations (PDEs) such as the Navier--Stokes (NS) equations remains computationally intensive, especially when implicit time integration is used to capture multiscale flow dynamics. This work…

Fluid Dynamics · Physics 2025-08-29 Shaobo Yao , Zhiyu Duan , Ziteng Wang , Wenwen Zhao , Shiying Xiong

An effort has been made to solve the Cauchy problem of the Navier-Stokes equations in the whole space by two methods. It is proved that the sum of the three vorticity components is a time-invariant in fluid motion. It has been proved that,…

Fluid Dynamics · Physics 2014-09-18 F. Lam

We consider a finite-volume domain $\mathfrak{D}\subset\mathbb{R}^{3}$ of size $\mathrm{Vol}(\mathfrak{D})\sim \mathrm{L}^{3}$ containing a viscous fluid of kinematic viscosity $\nu$ with velocity field $U_{a}(x,t)$ satisfying the…

Mathematical Physics · Physics 2025-11-18 Steven D Miller

The paper addresses an error analysis of an Eulerian finite element method used for solving a linearized Navier--Stokes problem in a time-dependent domain. In this study, the domain's evolution is assumed to be known and independent of the…

Numerical Analysis · Mathematics 2024-08-26 Michael Neilan , Maxim Olshanskii

Cavitation is a complex multiphase phenomenon characterised by vapour bubbles forming due to a sudden pressure drop and is often accompanied by increased hull vibrations, increased radiated noise and decrease in propeller and impeller…

Fluid Dynamics · Physics 2024-05-02 Dhruv Apte , Mingming Ge , Olivier Coutier-Delgosha

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

The paper introduces a geometrically unfitted finite element method for the numerical solution of the tangential Navier--Stokes equations posed on a passively evolving smooth closed surface embedded in $\mathbb{R}^3$. The discrete…

Numerical Analysis · Mathematics 2023-10-16 Maxim A. Olshanskii , Arnold Reusken , Paul Schwering

This work proposes a new stabilized $P_1\times P_0$ finite element method for solving the incompressible Navier--Stokes equations. The numerical scheme is based on a reduced Bernardi--Raugel element with statically condensed face bubbles…

Numerical Analysis · Mathematics 2023-04-06 Yuwen Li , Ludmil Zikatanov

It is well known that Boussinesq turbulent-viscosity hypothesis can introduce uncertainty in predictions for complex flow features such as separation, reattachment, and laminar-turbulent transition. This study adopts a recent physics-based…

Fluid Dynamics · Physics 2022-10-19 Minghan Chu , Xiaohua Wu , David E. Rival

The Volume-Averaged Navier-Stokes equations are used to study fluid flow in the presence of fixed or moving solids such as packed or fluidized beds. We develop a high-order finite element solver using both forms A and B of these equations.…

Numerical Analysis · Mathematics 2023-02-20 Toni El Geitani , Shahab Golshan , Bruno Blais

We present a stabilized finite element method for the numerical solution of cavitation in lubrication, modeled as an inequality-constrained Reynolds equation. The cavitation model is written as a variable coefficient saddle-point problem…

Numerical Analysis · Mathematics 2018-05-09 Tom Gustafsson , K. R. Rajagopal , Rolf Stenberg , Juha Videman

We present the Fully cOUpled loCAl model of sUperfLuid Turbulence (FOUCAULT) that describes the dynamics of finite temperature superfluids. The superfluid component is described by the vortex filament method while the normal fluid is…

Fluid Dynamics · Physics 2020-03-10 Luca Galantucci , Andrew W. Baggaley , Carlo F. Barenghi , Giorgio Krstulovic

In this article, we present a cut finite element method for two-phase Navier-Stokes flows. The main feature of the method is the formulation of a unified continuous interior penalty stabilisation approach for, on the one hand, stabilising…

Numerical Analysis · Computer Science 2019-05-01 Susanne Claus , Pierre Kerfriden

In this visualisation the instantaneous local velocity is expressed in terms of four components to capture the development of and interactions between coherent structures in turbulent flows. It is then possible to isolate the terms linked…

Fluid Dynamics · Physics 2009-10-13 Trinh Khanh Tuoc

The paper develops a solver based on a conforming finite element method for a 3D--1D coupled incompressible flow problem. New coupling conditions are introduced to ensure a suitable bound for the cumulative energy of the model. We study the…

Computational Physics · Physics 2013-04-08 Tatiana K. Dobroserdova , Maxim A. Olshanskii

Lagrangian tracer particle trajectories for invariant solutions of the Navier-Stokes equations confined to the three-dimensional geometry of plane Couette flow are studied. Treating the Eulerian velocity field of an invariant solution as a…

Fluid Dynamics · Physics 2024-12-09 John R. Elton , Predrag Cvitanović , Jonathan Halcrow , John F. Gibson