A Novel Method for the Numerical Solution of the Navier-Stokes Equations in Two-Dimensional Flow Using a Pressure Poisson Equation

2009 ◽  
Author(s):  
G. T. Messaris ◽  
C. A. Papastavrou ◽  
V. C. Loukopoulos ◽  
G. T. Karahalios ◽  
George Maroulis ◽  
...  
Keyword(s):  
Numerical Solution ◽  
Poisson Equation ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Pressure Poisson Equation ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Novel Method

An Exact Solution of the Unsteady Navier-Stokes Equations Resulting From a Stretching Surface

1994 ◽  
Vol 61 (3) ◽  
pp. 629-633 ◽  
Author(s):  
S. H. Smith
Keyword(s):  
Exact Solution ◽  
Stokes Equations ◽  
Limited Range ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Stretching Surface ◽  
Navier Stokes Equations ◽  
Short Period ◽  
Two Dimensional Flow ◽  
Surrounding Fluid

When a stretching surface is moved quickly, for a short period of time, a pulse is transmitted to the surrounding fluid. Here we describe an exact solution in terms of a similarity variable for the Navier-Stokes equations which represents the effect of this pulse for two-dimensional flow. The unusual feature is that this solution is only valid for a limited range of the Reynolds number; outside this domain unbounded velocities result.

scholarly journals Two-Dimensional Computational Model for Wave Rotor Flow Dynamics

1997 ◽  
Vol 119 (4) ◽  
pp. 978-985 ◽  
Author(s):  
G. E. Welch
Keyword(s):  
Stokes Equations ◽  
Flow Simulation ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Wave Rotor ◽  
Navier Stokes Equations ◽  
Flow Features ◽  
Rotor Experiment ◽  
Two Dimensional Flow ◽  
Rotor Flow

A two-dimensional (θ, z) Navier–Stokes solver for multiport wave rotor flow simulation is described. The finite-volume forms of the unsteady thin-layer Navier–Stokes equations are integrated in time on multiblock grids that represent the stationary inlet and outlet ports and the moving rotor passages of the wave rotor. Computed results are compared with three-port wave rotor experimental data. The model is applied to predict the performance of a planned four-port wave rotor experiment. Two-dimensional flow features that reduce machine performance and influence rotor blade and duct wall thermal loads are identified.

scholarly journals Turbulent 2.5-dimensional dynamos

2016 ◽  
Vol 799 ◽  
pp. 246-264 ◽  
Author(s):  
K. Seshasayanan ◽  
A. Alexakis
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Two Dimensional Flow

We study the linear stage of the dynamo instability of a turbulent two-dimensional flow with three components $(u(x,y,t),v(x,y,t),w(x,y,t))$ that is sometimes referred to as a 2.5-dimensional (2.5-D) flow. The flow evolves based on the two-dimensional Navier–Stokes equations in the presence of a large-scale drag force that leads to the steady state of a turbulent inverse cascade. These flows provide an approximation to very fast rotating flows often observed in nature. The low dimensionality of the system allows for the realization of a large number of numerical simulations and thus the investigation of a wide range of fluid Reynolds numbers $Re$, magnetic Reynolds numbers $Rm$ and forcing length scales. This allows for the examination of dynamo properties at different limits that cannot be achieved with three-dimensional simulations. We examine dynamos for both large and small magnetic Prandtl-number turbulent flows $Pm=Rm/Re$, close to and away from the dynamo onset, as well as dynamos in the presence of scale separation. In particular, we determine the properties of the dynamo onset as a function of $Re$ and the asymptotic behaviour in the large $Rm$ limit. We are thus able to give a complete description of the dynamo properties of these turbulent 2.5-D flows.

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