scholarly journals Two-Level Brezzi-Pitkäranta Discretization Method Based on Newton Iteration for Navier-Stokes Equations with Friction Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Rong An ◽  
Xian Wang
Keyword(s):  
Boundary Conditions ◽  
Iteration Method ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Newton Iteration ◽  
Navier Stokes ◽  
Discretization Method ◽  
Navier Stokes Equations ◽  
Stabilized Finite Element Method ◽  
The Stability

We present a new stabilized finite element method for Navier-Stokes equations with friction slip boundary conditions based on Brezzi-Pitkäranta stabilized method. The stability and error estimates of numerical solutions in some norms are derived for standard one-level method. Combining the techniques of two-level discretization method, we propose two-level Newton iteration method and show the stability and error estimate. Finally, the numerical experiments are given to support the theoretical results and to check the efficiency of this two-level iteration method.

Gyrotactic bioconvection at pycnoclines

2013 ◽  
Vol 733 ◽  
pp. 245-267 ◽  
Author(s):  
A. Karimi ◽  
A. M. Ardekani
Keyword(s):  
Boundary Conditions ◽  
Large Scale ◽  
Stokes Equations ◽  
Lewis Number ◽  
Boussinesq Approximation ◽  
Dynamical Behaviour ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
The Stability ◽  
Micro Organisms

AbstractBioconvection is an important phenomenon in aquatic environments, affecting the spatial distribution of motile micro-organisms and enhancing mixing within the fluid. However, stratification arising from thermal or solutal gradients can play a pivotal role in suppressing the bioconvective flows, leading to the aggregation of micro-organisms and growth of their patchiness. We investigate the combined effects by considering gyrotactic motility where the up-swimming cells are directed by the balance of the viscous and gravitational torques. To study this system, we employ a continuum model consisting of Navier–Stokes equations with the Boussinesq approximation coupled with two conservation equations for the concentration of cells and stratification agent. We present a linear stability analysis to determine the onset of bioconvection for different flow parameters. Also, using large-scale numerical simulations, we explore different regimes of the flow by varying the corresponding boundary conditions and dimensionless variables such as Rayleigh number and Lewis number ($\mathit{Le}$) and we show that the cell distribution can be characterized using the ratio of the buoyancy forces as the determinant parameter when $\mathit{Le}\lt 1$ and the boundaries are insulated. But, in thermally stratified fluids corresponding to $\mathit{Le}\gt 1$, temperature gradients are demonstrated to have little impact on the bioconvective plumes provided that the walls are thermally insulated. In addition, we analyse the dynamical behaviour of the system in the case of persistent pycnoclines corresponding to constant salinity boundary conditions and we discuss the associated inhibition threshold of bioconvection in the light of the stability of linearized solutions.

The Patch Test of Numerical Manifold Schemes with Mixed Cover Coupled Velocity and Pressure for Steady N-S Equations

2011 ◽  
Vol 378-379 ◽  
pp. 68-71
Author(s):  
Shu Ping Chen ◽  
Zheng Rong Zhang ◽  
Jin Hua Yan
Keyword(s):  
Patch Test ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Stability Conditions ◽  
Direct Solution ◽  
Navier Stokes Equations ◽  
Cover System ◽  
The Stability ◽  
Numerical Manifold

In numerical manifold schemes for direct solution of steady Navier-Stokes equations, mixed cover for velocity and pressure was adopted in finite element cover system. The patch test of numerical schemes was investigated, mixed cover manifold element has been proved to meet the stability conditions, and can be applied to directly solve Navier-Stokes equations coupled velocity and pressure. As an application, the numerical manifold schemes were used to simulate the steady flow past a step. Numerical solutions illustrate the stability of numerical manifold schemes, and it indicates that manifold method is an effective numerical method for steady Navier-Stokes equations.

scholarly journals Ensemble Algorithm for Parametrized Flow Problems with Energy Stable Open Boundary Conditions

2020 ◽  
Vol 20 (3) ◽  
pp. 531-554
Author(s):  
Aziz Takhirov ◽  
Jiajia Waters
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Initial Conditions ◽  
Navier Stokes ◽  
Open Boundary ◽  
Open Boundary Conditions ◽  
Navier Stokes Equations ◽  
Flow Problems ◽  
The Stability ◽  
Ensemble Calculation

AbstractWe propose novel ensemble calculation methods for Navier–Stokes equations subject to various initial conditions, forcing terms and viscosity coefficients. We establish the stability of the schemes under a CFL condition involving velocity fluctuations. Similar to related works, the schemes require solution of a single system with multiple right-hand sides. Moreover, we extend the ensemble calculation method to problems with open boundary conditions, with provable energy stability.

scholarly journals Nonlinear Taylor vortices and their stability

1981 ◽  
Vol 102 ◽  
pp. 249-261 ◽  
Author(s):  
C. A. Jones
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Rotating Cylinders ◽  
Navier Stokes Equations ◽  
Taylor Vortices ◽  
The Stability ◽  
Axisymmetric Perturbations

Axisymmetric numerical solutions of the Navier–Stokes equations for flow between rotating cylinders are obtained. The stability of these solutions to non-axisymmetric perturbations is considered and the results of these calculations are compared with recent experiments.

New boundary conditions in the transition régime

1968 ◽  
Vol 2 (3) ◽  
pp. 293-310 ◽  
Author(s):  
Carlo Cercignani ◽  
Gino Tironi
Keyword(s):  
Boundary Conditions ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Slip Flow ◽  
Navier Stokes ◽  
Main Body ◽  
Parallel Plates ◽  
Navier Stokes Equations ◽  
Concentric Cylinders ◽  
Flow Heat

Starting from the Boltzmann equation, new boundary conditions are derived to be matched with the Navier—Stokes equations, that are supposed to hold in the main body of a gas. The idea upon which this method is based goes back to Maxwell and Langmuir. Since the distribution function is supposed to be completely determined by the Navier—Stokes equations, this new set of boundary conditions extends in some sense the validity of the macroscopic equations to the transition and free molecular régimes. In fact, it is shown that the free molecular and slip flow régimes are correctly described by this method; the latter is also supposed to give a reasonable approximation for the complete range of Knudsen numbers. The new procedure is applied to different problems such as plane Couette flow, plane and cylindrical Poiseuile flow, heat transfer between parallel plates and concentric cylinders. Results are obtained and compared with the exact numerical solutions for the above-mentioned problems.

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