scholarly journals Navier–Stokes equations with periodic boundary conditions and pressure loss

2007 ◽  
Vol 20 (1) ◽  
pp. 48-53 ◽  
Author(s):  
Chérif Amrouche ◽  
Macaire Batchi ◽  
Jean Batina
Keyword(s):  
Boundary Conditions ◽  
Pressure Loss ◽  
Periodic Boundary ◽  
Stokes Equations ◽  
Periodic Boundary Conditions ◽  
Navier Stokes ◽  
Navier Stokes Equations

scholarly journals Probabilistic Methods for the Incompressible Navier–Stokes Equations With Space Periodic Conditions

2013 ◽  
Vol 45 (3) ◽  
pp. 742-772
Author(s):  
G. N. Milstein ◽  
M. V. Tretyakov
Keyword(s):  
Boundary Conditions ◽  
Numerical Integration ◽  
Periodic Boundary ◽  
Stokes Equations ◽  
Weak Sense ◽  
Periodic Boundary Conditions ◽  
Probabilistic Methods ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Probabilistic Nature

We propose and study a number of layer methods for Navier‒Stokes equations (NSEs) with spatial periodic boundary conditions. The methods are constructed using probabilistic representations of solutions to NSEs and exploiting ideas of the weak sense numerical integration of stochastic differential equations. Despite their probabilistic nature, the layer methods are nevertheless deterministic.

scholarly journals Limits of the Stokes and Navier–Stokes equations in a punctured periodic domain

2019 ◽  
Vol 18 (02) ◽  
pp. 211-235
Author(s):  
Michel Chipot ◽  
Jérôme Droniou ◽  
Gabriela Planas ◽  
James C. Robinson ◽  
Wei Xue
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Stokes Equations ◽  
Periodic Boundary Conditions ◽  
Dirichlet Boundary Conditions ◽  
Navier Stokes ◽  
Periodic Domain ◽  
Navier Stokes Equations ◽  
Forcing Function ◽  
Connected Set

We treat three problems on a two-dimensional “punctured periodic domain”: we take [Formula: see text], where [Formula: see text] and [Formula: see text] is the closure of an open connected set that is star-shaped with respect to [Formula: see text] and has a [Formula: see text] boundary. We impose periodic boundary conditions on the boundary of [Formula: see text], and Dirichlet boundary conditions on [Formula: see text]. In this setting we consider the Poisson equation, the Stokes equations, and the time-dependent Navier–Stokes equations, all with a fixed forcing function [Formula: see text], and examine the behavior of solutions as [Formula: see text]. In all three cases we show convergence of the solutions to those of the limiting problem, i.e. the problem posed on all of [Formula: see text] with periodic boundary conditions.

scholarly journals Numerical Simulation of 3D Flow over a Circular Cylinder

2021 ◽  
Vol 2057 (1) ◽  
pp. 012072
Author(s):  
A N Kusyumov ◽  
S A Kusyumov ◽  
S A Mikhailov ◽  
E V Romanova
Keyword(s):  
Circular Cylinder ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Stokes Equations ◽  
Spectral Characteristics ◽  
Periodic Boundary Conditions ◽  
Circular Cylinders ◽  
Navier Stokes ◽  
3D Flow ◽  
Navier Stokes Equations

Abstract Unsteady 3D flow over a circular cylinder at Reynolds number of 3900 is studied numerically using the Navier-Stokes equations. Two formulations of the problem were considered: with boundary conditions corresponding to the flow around an isolated cylinder and with periodic boundary conditions to the flow behind a parallel circular cylinders grid. A comparative analysis of the integral and distributed characteristics of the flow around the cylinder and the spectral characteristics of the flow for both formulations of the problem is carried out.

scholarly journals Probabilistic Methods for the Incompressible Navier–Stokes Equations With Space Periodic Conditions

2013 ◽  
Vol 45 (03) ◽  
pp. 742-772 ◽  
Author(s):  
G. N. Milstein ◽  
M. V. Tretyakov
Keyword(s):  
Boundary Conditions ◽  
Numerical Integration ◽  
Periodic Boundary ◽  
Stokes Equations ◽  
Weak Sense ◽  
Periodic Boundary Conditions ◽  
Probabilistic Methods ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Probabilistic Nature

We propose and study a number of layer methods for Navier‒Stokes equations (NSEs) with spatial periodic boundary conditions. The methods are constructed using probabilistic representations of solutions to NSEs and exploiting ideas of the weak sense numerical integration of stochastic differential equations. Despite their probabilistic nature, the layer methods are nevertheless deterministic.

Numerical Modeling of Unsteady Flow Through a Turbomachine Stage

1998 ◽  
Author(s):  
R. I. Issa ◽  
M. A. Sadri
Keyword(s):  
Numerical Method ◽  
Periodic Boundary ◽  
Stokes Equations ◽  
Unsteady Flows ◽  
Periodic Boundary Conditions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Sliding Mesh ◽  
Flow Through ◽  
Implicit Numerical Method

A numerical method is presented for the simulation of unsteady flows through turbomachine stages with unequal numbers of rotor and stator blades. The method solves the two-dimensional incompressible, unsteady, ensemble averaged, Navier-Stokes equations together with transport equations for the k–ϵ turbulence model employed to simulate the effects of turbulence. The method employs an implicit pressure-based finite volume discretisation procedure. In order to simulate the flow in the rotor and stator passages simultaneously, a sliding mesh methodology is developed which allows the mesh mapping the rotor domain to move in a sliding action relative to the static mesh which maps the stator passage. Phase-lagged periodic boundary conditions are implemented in the context of the implicit numerical method developed to handle unequal rotor and stator pitches efficiently. The effectiveness and accuracy of the method are assessed against data for a rotor/stator configuration with unequal pitches in adjacent rows of a low speed turbine.

Parallel iterative finite-element algorithms for the Navier–Stokes equations with nonlinear slip boundary conditions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Kangrui Zhou ◽  
Yueqiang Shang
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Parallel Algorithms ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Parallel Iterative ◽  
Nonlinear Slip Boundary Conditions

AbstractBased on full domain partition, three parallel iterative finite-element algorithms are proposed and analyzed for the Navier–Stokes equations with nonlinear slip boundary conditions. Since the nonlinear slip boundary conditions include the subdifferential property, the variational formulation of these equations is variational inequalities of the second kind. In these parallel algorithms, each subproblem is defined on a global composite mesh that is fine with size h on its subdomain and coarse with size H (H ≫ h) far away from the subdomain, and then we can solve it in parallel with other subproblems by using an existing sequential solver without extensive recoding. All of the subproblems are nonlinear and are independently solved by three kinds of iterative methods. Compared with the corresponding serial iterative finite-element algorithms, the parallel algorithms proposed in this paper can yield an approximate solution with a comparable accuracy and a substantial decrease in computational time. Contributions of this paper are as follows: (1) new parallel algorithms based on full domain partition are proposed for the Navier–Stokes equations with nonlinear slip boundary conditions; (2) nonlinear iterative methods are studied in the parallel algorithms; (3) new theoretical results about the stability, convergence and error estimates of the developed algorithms are obtained; (4) some numerical results are given to illustrate the promise of the developed algorithms.

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